Statıstıcs II (ENG) - İşletme (İngilizce)

Ünite 1

Soru 1

Population of country A is 500.000, population of males is 240.000 (25 % are students), population of females is 260.000 (30 % are students). How many people are there in the target population for a survey to determine sports habits of students?

260.000

240.000

138.000

78.000

60.000

Açıklama:

x = 240.000 . 0.25 + 260.000 . 0.30 = 138.000. pg. 3. Correct answer is C.

Doğru Cevap: C

Soru 2

Population of university A is 20000, population of engineering students is 5000 (25 % take statistics course), population of psychology students is 400 (25 % take statistics course), population of statistics students is 400. How many people are there in the target population for a survey about statistics courses?

5800

5400

1750

1350

400

I. A population should be finite
II. Sometimes sample may be bigger than population
III. Using a proper sample surveyors may make very accurate prediction
Which one(s) of the above is/are true?

I, II

II, III

I, III

III

The population consist of five cities denoted by A, B, C, D, and E. If a sample of two cities is to be selected from this population how many different samples can be created?

I. Simple Random Sampling
II. Stratified Sampling
III.Convenience Sampling
IV. Quota Sampling
In which of the method(s) above target population is divided into subgroups?

I, II

I, III

II, III

II, IV

Açıklama:

In Quota sampling and Stratified sampling the population is divided into subgroups.

Doğru Cevap: D

Soru 31

A survey to search out the preferences of teenagers in Istanbul about novel selection was conducted accordingly: 80 girls and 80 boys, aged between 14-18, were asked the same questions such as the last novel they read, etc. For the design of the study, which is a wrong statement?

Target population is the teenagers in Istanbul

80 girls and 80 boys, aged between 14-18 are the sample

Sample reflects the characteristics of the population in the best way possible

Purpose of the survey is to find out the preferances of teenagers in Istanbul about novel selection

Teenagers from all over the world can also be accepted as the population

Açıklama:

Target population is whom the results obtained from the sample are to be applied or generalized. Sample should reflect the characteristics of the population (teenagers) as much as possible. In the case represented in the question, gender distribution of the population was not taken into consideration and simplu thought to be half and half.
Characteristics like gender distribution should be considered while designing such a study.

Doğru Cevap: C

Soru 32

A qualitative survey was conducted to find out how contended 3rd year medical students are with distance learning instead of conventional methods in Europe. 250 students were included in the study from different European countries. Concerning statistical terminology, which of the following matching is true?

Target population - 3rd year medical students in Europe

Sample - Medical students in Europe

Purpose - to learn the difference between distance learning and conventional methods

Sampling - Reflection of the results to whole population

Random sample - Choosing students from all grades

Açıklama:

Target population is whom the results obtained from the sample are to be applied or generalized. Population is the universe to be sampled. Sample is a part of a population which is provided by some process or other, usually by deliberate selection with the object of investigating the properties of the parent population or set (for the question, 250 students from different European countries). Purpose is to figure out how contended 3rd year medical students are with distance learning instead of conventional methods in Europe. Sampling is technique of selecting items from a population. Random sample is the sample taken from the population including the characteristics of the population as much as possible.
Target population in the question is the 3rd year medical students in Europe.

Doğru Cevap: A

Soru 33

Why to use a sample instead of a census to obtain some information about the characteristics of a population?

A census often provides reliable and useful information at much lower cost than does a sampling.

A sampling survey often provides more timely information than a census.

While a sample data is gathered, many unexpected problems may affect the accuracy of the results.

Some populations are uncountable or infinite to conduct a sample.

If a test includes the destruction of an item or product, a census should be used.

Açıklama:

A sampling survey often provides more timely information than a census, because fewer data have to be collected and analysed. Statements in the other choices are exact opposite expressions concerning survey and census.

Doğru Cevap: B

Soru 34

Which one of the following option is a non-probability sampling method?

Systematic Sampling

Cluster Sampling

Stratified Sampling

Simple Random Sampling

Convenience Sampling

Açıklama:

Convenience Sampling is one of the non-probability sampling methods while the methods included in the other choices are examples of probability sampling methods.
Convenience Sampling is one of the non-probability sampling methods.

Doğru Cevap: E

Soru 35

Which sampling method should be chosen when each possible sample combination of the specified size required to has equal probability of being chosen?

Stratified Sampling

Cluster Sampling

Systematic Sampling

Random sample

Snowball Sampling

Açıklama:

With the random sample method, each possible sample combination of the specified size has equal probability of being chosen.
Random sample is the method to be chosen when each possible sample combination of the specified size required to has equal probability of being chosen.

Doğru Cevap: D

Soru 36

If you want to conduct a research to assess newspaper reading habit of people older than age 30 in a particular village, and want to discuss the results according to gender, socioeconomic status (regarding the income less and more than a predetermined amount) and being a university-graduate or not, which sampling method will be the best choice?

Stratified Sampling

Using Random Numbers for Sample Selection

Cluster Sampling

Systematic Sampling

Snowball Sampling

Açıklama:

In stratified sampling method, the target population is divided into homogenous subgroups. Subgroups should be determined based on available characteristics that they are related to the outcome of the survey or research. When a population can be clearly divided into homogenous groups based on some characteristic, we can use stratified random sampling.
If the study design includes subgroups, stratified sampling method should be chosen.

Doğru Cevap: A

Soru 37

Which sampling method relies on naturally occurring group of units in the population?

Simple Random Sampling

Using Random Numbers for Sample Selection

Stratified Sampling

Cluster Sampling

Systematic Sampling

Açıklama:

A cluster is a naturally occurring group of units in the population. Cluster sampling method differs from other sampling methods in that the clusters naturally occur in a population.
Cluster sampling method relies on naturally occurring group of units in the population.

Doğru Cevap: D

Soru 38

Which sampling method provides observation of habits, opinions, and viewpoints in the easiest possible manner?

Systematic Sampling

Convenience Sampling

Cluster Sampling

Snowball Sampling

Quota Sampling

Açıklama:

A convenience sample involves a group of individuals that is ready and available. The surveyors select members merely on the basis of proximity and does not consider whether they represent the entire population or not. By using this sampling techniques, we can observe habits, opinions, and viewpoints in the easiest possible manner.
Convenience Sampling provides observation of habits, opinions, and viewpoints in the easiest possible manner.

Doğru Cevap: B

Soru 39

In a social experiment about drug abuse in young population, researchers have difficulities to list the population, even to reach them. Which sampling method should they use for the research?

Snowball Sampling

Quota Sampling

Convenience Sampling

Cluster Sampling

Stratified Sampling

Açıklama:

Snowball sampling technique is used when listing of population is not available and cannot be compiled. The identified subjects are asked to recruit other members and then those people are asked to recruit, and so on.

Doğru Cevap: A

Soru 40

If a research team have a suspicion that sampling may lead to a bias, which sampling method is most likely the one used in the study?

Stratified Sampling

Cluster Sampling

Snowball Sampling

Quota sampling

Convenience Sampling

Açıklama:

In Snowball Sampling, an unbiased sample may not be obtained because of recommendations.
In the study design mentioned in the question, the concern comes from the Snowball Sampling.

Doğru Cevap: C

Soru 41

Which of the following is not one of the reasons for sampling from a population?

Testing of a unit may be too expensive and testing the whole population may exceed the limit of the fund allocated

Measuring time may be too long to measure all the units in the population and a complete measurement takes for ages

A full inspection of the aggregate data may be troublesome while a good sample reflects the population with less effort

Reaching all the population is sometimes impossible and most of the researches do not require a complete set

Using a manipulated sample makes it easier to create a fake population that does not reflect the facts of reality

Açıklama:

The reasons for sampling from a population are
- the limitations on costs and time,
- physical impossibilities of reaching all the members of a population,
- the accuracy problems of complete testing, and
- some tests being destructive.
On the other hand, faking the facts of a population can not be the reason why the sampling is needed.

Doğru Cevap: E

Soru 42

if you want to take a random sample from the population, what should be done for an accurate sample?

Including the characteristics of the population as much as possible

Taking the samples that can be reached easily

Ignoring some of the characteristics that makes it harder to sample

Being quick to get the testing phase as soon as possible

Spending less effort while sampling and saving it to the analysis

Açıklama:

if you want to take a random sample from a population, you would like to include the characteristics of the population in your sample as much as possible. Alternative B, C, D and E are the DO NOTs of the sampling process.

Doğru Cevap: A

Soru 43

A researcher wants to conduct a survey to determine the infertility rate in females over 30 years of age living in Turkey. Which of the following is the true target population for this research?

All females over 30 age of years living in Ankara

All females living in Turkey

All people living in Turkey

All females over 30 age of years living in Turkey

All people over 30 age of years living in Turkey

Açıklama:

"All females over 30 age of years living in Turkey" is the true target population for the research given in the question.

Doğru Cevap: D

Soru 44

Which of the following is correct about the sampling process?

Sample must be the census of the population

Sampling size can not be over 1% of the population

Sample must include all members of the population

Sample must include at most half of members of the population

Sample must represent or model of the population

Açıklama:

In the sampling process, the sample taken must represent or model of the population.

Doğru Cevap: E

Soru 45

In stratified sampling method, the target population is synthetically divided into homogenous subgroups based on some characteristics. Which of the following is the correct term for these homogeneous subgroups?

Stratum

Frame

Strasse

Strata

Stripe

Açıklama:

In stratified sampling method, the target population is divided into homogenous subgroups which are called strata. Each subgroup is called stratum. Alternatives other than strata and stratum are irrelevant to the question, and the plural term for the subgroups "strata" is the correct term for the question.

Doğru Cevap: D

Soru 46

What is the difference between stratified and cluster sampling?

In stratified sampling groups characteristics designed by the researcher while in the clustering they occur naturally

Stratified sampling is a random sampling method while clustered sampling is a non-probability sampling method

Stratified sampling method is always more accurate than clustered sampling

Clustering method requires subgroup segmentation by the researcher, while stratified sampling does not

Cluster sampling is more efficient than simple random sampling, while the stratified sampling is not

Açıklama:

If there are 120 objects in a population and the investigator wants to use simple random sampling to choose objects in to a sample from this population, what is the probability of a object to be selected in to a sample?

120/4

120/10

1/100

1/120

1/100

Açıklama:

any types of probability samples are available for sampling from a population. The most basic sampling method is the simple random sampling. The simple random sample from a population is a sample that is selected so that each possible sample combination of the specified size has equal probability of being chosen. In practice, a simple random sample is usually called random sample.

Select the first sample element by giving each of the N population elements an equal probability (1/N) of being chosen.

Populations are always finite.

The size of the population is smaller than the sample.

Populations always contain more than 1000 items.

Populations can contain any type of objects.

Açıklama:

Populations can be heterogenous or infinite. So arguments in A and B are not true. Population size is larger than the sample, so C is false also. There is no restriction on population size, so D is false. However, populatios can contain any type of objects. So E is true.

Doğru Cevap: E

Soru 63

Which of the following are among the reasons for sampling?

Cost
Time
Accuracy
Destructive tests
Esthetics

II, III, IV and V

I, III, IV and V

I, II, IV and V

I, II, III and IV

I, II, III and V

Açıklama:

Esthetics is not a reason for sampling.

Doğru Cevap: D

Soru 64

In which sampling methods one uses stratums?

Simple random sampling

Stratified sampling

Sampling with replacement

Cluster sampling

Systematic sampling

Açıklama:

Stratums are used in stratified sampling.

Doğru Cevap: B

Soru 65

In which of the following sampling methods subgroups occur naturally (such as departments of a company)?

Stratified sampling

Cluster sampling

Systematic sampling

Snowball sampling

Convenience sampling

Açıklama:

In cluster sampling the subgroups occur naturally. These subgroups are called clusters.

Doğru Cevap: B

Soru 66

A researcher wants to compute the mean weight of a certain product produced by a firm. The firm produces 8000 products per day and each product has a serial number from 1 to 8000. The researcher decide to choose 80 products in order to compute average weight. He chooses the products with serial numbers 3, 103, 203,303, 403, 503......7903. Which method of sampling did the researcher apllied?

Systematic sampling

Cluster sampling

Stratified sampling

Sampling with replacement

Convenience sampling

Açıklama:

He used the systematic sampling because he chooses 1 of the every 100 products in a systematic way. (8000/80=100 so he chooses the first element randomly, which is the 3rd one, and adds 100 to find the next one at each time)

Doğru Cevap: A

Soru 67

In which sampling methods the sample includes the individiuals which are ready and availiable?

Quota sampling

Snowball sampling

Convenience sampling

Cluster sampling

Systematic sampling

Açıklama:

A convenience sample involves a group of individuals that is ready and available. It is also called availability sampling method.

Doğru Cevap: C

Soru 68

A reseacher wants to analyse the consumption behaviors of people in a city. He divides the population into 4 groups: male/female and young/old. Then he estimates the proportion of each group in population and constructs the samples accordingly. So, which sampling method does he uses?

Quota sampling

Simple random sampling

Systematic sampling

Cluster sampling

Stratified sampling

Açıklama:

The researcher is dividing the population to groups, so he is uing the quota method.

Doğru Cevap: A

Soru 69

"In _________________ sampling method, the members, who are identified previously, are asked to identify other members of the population. As newly identified members name others, the sample is getting larger." Which of the following completes the blank in given sentence?

Cluster

Systematic

Simple random

Stratified

Snowball

Açıklama:

The defined method is snowball sampling method, as the sample gets larger like a snowball.

Doğru Cevap: E

Soru 70

Doğru Cevap: D

Soru 8

Interval estimation : the limits of the confidence interval are (99, 123), the significance level is 0.01. What is the sample arithmetic mean?

104

111

112

114

117

Açıklama:

x = (99 + 123) / 2 = 111. pg. 33. Correct answer is B.

Doğru Cevap: B

Soru 9

Interval estimation : the limits of the confidence interval are (4.1, 5.9), the significance level is 0.05. What is the sample arithmetic mean?

4.15

4.60

5.00

5.30

Soru 28

Interval estimation : the limits of the confidence interval are (397, 555), the significance level is 0.05. What is the sample arithmetic mean?

476

421

452

463

484

Açıklama:

x = (397 + 555) / 2 = 476. pg. 33. Correct answer is A.

Doğru Cevap: A

Soru 29

Interval estimation : the limits of the confidence interval are (0.41, 0.97), the significance level is 0.01. What is the sample arithmetic mean?

0.78

0.69

0.71

0.73

Interval estimation problem : the population standard deviation is not known, the sample standard deviation is 36, there are 9 observations in the sample. What is the value of the standard error to calculate the confidence interval?

Açıklama:

st err = st dev / (n)^1/2 = 36 / (9)^1/2 = 12. pg. 38 Correct answer is A.

Doğru Cevap: A

Soru 51

For age variable the following sample data is gathered: 45, 47, 42, 40, and 51. What is the point estimate of the population arithmetic mean for variable age?

Açıklama:

We need to calculate the sample arithmetic mean, it is equal to 45.

Doğru Cevap: A

Soru 52

In poin estimation, What is sample statistic called for population parameter?

Predicted

Estimate

Final value

Data

Variability

Açıklama:

To obtain information about a population parameter, such as the value of population mean μ or population proportion π, a random sample of objects from the population is usually created. Then, the sample statistic found from the values of the sample observations is used for predictions about population parameter. This sample statistic is called an estimate of the population parameter.

Doğru Cevap: B

Soru 53

The process of estimating a population parameter by a single number derived from the sample is called _______________ estimation?

Default

Unknown

Interval

Variable

Point

Açıklama:

The process of estimating a population parameter by a single number derived from the sample is called point estimation.

Doğru Cevap: E

Soru 54

___________________________, denoted by π, is the proportion of the members/objects/individuals of a population that have a specific characteristic of interest?

A population arithmetic mean

Sample arithmetic mean

Sample standard deviation

Population Variance

A population proportion

Açıklama:

A population proportion, denoted by π, is the proportion of the members/objects/individuals of a population that have a specific characteristic of interest.

Doğru Cevap: E

Soru 55

the government policy planner is selected 4000 people from the population using cluster sampling, clusters are organized according to the geographical regions. Then, planner is found that the 1000 people in the sample live under the poverty threshold. What is the point estimate of the population proportion?

0.75

0.25

0.50

0.15

0.90

Açıklama:

p = f/n
In the equation, f is the sample frequency and n is the sample size.
In order find the point estimate
1000/4000=0.25.

Doğru Cevap: B

Soru 56

____________________________ is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.

The sampling distribution of the sample variance

The sampling distribution of the sample standard deviation

The sampling distribution of the sample mean

The sampling distribution of the sample median

The sampling distribution of the sample mode

Açıklama:

The sampling distribution of the sample mean is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.

Doğru Cevap: C

Soru 57

In a population there are 5 observations as follows: 10, 90, 20, 80, 50. What is the arithmetic mean of the sampling distribution of the sample mean for all the samples with the size 2?

100

Açıklama:

It will be equal to the population arithmetic mean and the population arithmetic mean in this problem is 50.

Doğru Cevap: A

Soru 58

The standard deviation of the sampling distribution of the sample mean is ___________ than the population standard deviation?

equal

bigger

smaller

over

missing

Açıklama:

the standard deviation of the sampling distribution of the sample mean is smaller than the population standard deviation.

Doğru Cevap: C

Soru 59

In a population there are 5 observations, how many different samples of size 4 can be created from this population?

Açıklama:

Doğru Cevap: C

Soru 60

In an interval estimation problem for population arithmetic mean; z =1.96, population standard deviation =12, n=16 and sample arithmetic mean = 28. What is the upper limit of the confidence interval for population mean?

35.89

42.98

49.17

35.79

33.88

Açıklama:

Açıklama:

The test statistic is calculated according to this formula: z = (x −µ)/(σ / (n)^1/2 ). Here x=1900, µ=1000, σ=24, n=576, if we plug the numbers into the formula we would have z = (1020 −1000)/(24 / (576)^1/2 ) which is equal to 20
The answer is C

Doğru Cevap: C

Soru 19

I. The mean, median and mode of the t distribution are all equal to zero.
II. The t distribution is bell-shaped and symmetrical. The total area under a t-curve is 1 or 100%
III. As the degrees of freedom decreases, the shape of the t-distribution approaches to the standard normal distribution.
Which of the given statements about properties of the t-distribution are true?

Only I

Only II

I and II

I and III

II and III

Açıklama:

Certain properties of the t distribution are as follows:
• The t distribution is bell-shaped and symmetrical. The total area under a t-curve is 1 or 100%
• The mean, median and mode of the t distribution are all equal to zero.
• As the degrees of freedom increases, the shape of the t distribution approaches to the standard normal distribution.
The answer is C.

Doğru Cevap: C

Soru 20

For a statistical test following a normal distribution, the alternative hypothesis is that the mean equals to a hundred and the standard deviation is s = 20. A sample of 25 observations is randomly selected and the sample average is equal to 102. What is the test statistic equal to?

0.35

0.40

0.45

0.5

0.55

Açıklama:

The observation is equal to 25 which is less than 30, so we use this formula to calculate the test statistics: t = (x −µ)/(s / (n)^1/2). Here x=102, µ=100, s=20, n=25 this yields to t = (102 −100)/(20 / (25)^1/2) which is equal to 1/2=0.5
The answer is D.

Doğru Cevap: D

Soru 21

Identify the test statistic
Select a level of significance
State null and alternate hypotheses
Take a sample and make the decision
Formulate a decision rule

Which one of the following alternatives indicate the correct order of hypothesis testing steps?

I-III-II-IV-V

II-III-V-I-IV

III-II-I-V-IV

III-V-II-IV-I

IV-III-II-V-I

Açıklama:

Review the part 'Steps in Hypothesis Testing'
To test the claims made about the population parameters or in other words to test the statistical expressions the following steps can be followed:
Step 1: State null and alternate hypotheses
Step 2: Select a level of significance
Step 3: Identify the test statistic
Step 4: Formulate a decision rule
Step 5: Take a sample and make the decision

Doğru Cevap: C

Soru 22

What does the term '1-β' indicate?

Test power

Significance level

Type I error

Type II error

Rejection region

Açıklama:

Review the part 'Step 2: Select the Level of Significance'
Power of a statistical test can be calculated as 1- β.

Doğru Cevap: A

Soru 23

In an investigation, the probability of failing to reject the null hypothesis (H0) when it is false is 0.05. What is the test power in this study?

0.05

0.10

0.50

0.90

0.95

Açıklama:

Review the part 'Step 2: Select the Level of Significance'
The probability of failing to reject the null hypothesis (H0) when it is false is the definiton of type II error and it is 0.05.
Test power= 1- type II error.

Doğru Cevap: E

Soru 24

What is the critical value t0 for two-sided test with α = 0.05 and n = 22?

1.717

1.727

2.074

2.080

2.096

Açıklama:

Review the t distribution table at p.62
Look at the t distribution table at p.62
df=21
Significance level = 0.025 for one-sided
= 0.05 for two-sided

Doğru Cevap: D

Soru 25

What is the critical value zfor one-sided test with %90 confidence level?

1.29

1.65

1.96

2.58

2.72

Açıklama:

Review Table 3.2 at page 54

Doğru Cevap: A

Soru 26

In a hypothesis testing procedure, the population mean and standard deviation are 800 and 200 respectively. On the other hand, sample arithmetic mean of a random sample of 225 observations is 950. If this procedure is followed, what is the value of the observed z?

-11.25

-5.66

2.58

5.66

11.25

Açıklama:

Review the part 'HYPOTHESIS TESTING FOR THE POPULATION MEAN (LARGE SAMPLE)'
Use the z formula at page 58

Doğru Cevap: E

Soru 27

(Answer the question 7, 8 and 9 according to those information)
Consider the following hypothesis:
H0: μ = 80
H1: μ ≠ 80
A random sample of 16 observations is randomly selected from normally distributed population. The mean of the sample is 90 and the standard deviation of the sample is 5. Test the null hypothesis given above with %95 confidence level.
What is the critical value for that test procedure?

1.753

2.131

2.120

1.746

1.566

Açıklama:

In hypothesis testing, which of the steps below is the first to be followed?

Identify the test statistics

State null or alternate hypotheses

Formulate a decision rule

Select a level of significance

Take a sample and make a decision

Açıklama:

Doğru Cevap: B

Soru 34

In a production line, the mean weight of the products should be 450 grams and the standard deviation of the weight variable is σ = 25. It is known that the distribution of the weights of the packages follow a normal distribution. A sample of 32 observations is randomly selected from the production line in the afternoon and the sample average is found as of 448 grams.The significance level α = 0.05 for this problem.
If you follow the five step hypothesis testing procedure, what is the alternative hypothesis for the situation given above ?

The mean weight of the packages is 450 grams.

The mean weight of the packages is 448 grams.

the mean weight of the packages is not 450 grams.

The mean weight of the packages is less than 450 grams.

The mean weight of the packages is more than 450 grams.

Açıklama:

The null hypothesis (H0 ) is “the mean weight of the packages is 450 grams” and the alternative hypothesis (H1 ) is “the mean weight of the packages is less than 450 grams”. Here the alternative hypothesis is formed as a left tailed test because the given problem considers the weight of the packages than 450 grams.

Doğru Cevap: D

Which sign we are not going to use in one sample hypothesis problems for alternate hypothesis?

≠

Açıklama:

= sign is only used for the null hypothesis

Doğru Cevap: D

Soru 47

If you reject the null hypothesis when the null hypothesis is false, what is the decision?

Type I error

Type II error

1- β

Correct decision

Açıklama:

Doğru Cevap: E

Soru 48

what do we call "P(fail to reject the null hypothesis H₀ when it is actually false)"?

Correct decision

1-β

β + α

Açıklama:

through a hypothesis-testing, it is also important to consider the probability of a type II error, failing to reject the null hypothesis (H0) when it is false, which is denoted by β. Then the type II error probability is,
β = P(type I error) = P(fail to reject the null hypothesis H0 when it is actually false)

Doğru Cevap: E

Soru 49

what is the total size of the rejection region in hypothesis testing?

1- β

H0: μ = μ0

H1: μ ≠ μ0

1- α

Açıklama:

If the null hypothesis (H0) is rejected in a hypothesis test with the significance level α then it is said that statistical hypothesis test results are statistically significant at the α level. Determination of the significance level is specifying the rejection probability of the null hypothesis (H0) when it is actually true. The significance level α of a hypothesis test is determined by the researcher before the data collection. Often the level of significance α value of a hypothesis test is selected as 1%, 5% or 10%. When you choose the significance level, on practice, it means that if you repeatedly create many samples from the population in question, 1% of the time your results will not be correct.

Doğru Cevap: E

Soru 50

if the type I error is 0.05 and a two-sided hypothesis testin is investigated, what is the z value from the standard normal distribution table?

1.96

2.18

1.65

2.33

1.88

Açıklama:

0.95 / 2 = 0.4750
search 0.4750 from the table
the answer is 1.96

Doğru Cevap: A

Ünite 4

Açıklama:

The test statistic for a one-way ANOVA test is the ratio of two variances; namely the variance between samples (MSB) and variance within samples (MSW). Then, the test statistic F can be obtained as follows, F = MSB / MSW.
Then,
F = 350/70 = 5 . The correct answer is B.

Doğru Cevap: B

Soru 10

In a problem, the variance between samples is 200 and the test stastic F is 2. What is the variance within samples?

100

202

Açıklama:

Doğru Cevap: D

Soru 11

Which of the given forms of hypothesis equivalently is one that is correct?

H₀: µ₁ = µ₂
H₁: µ₁ ≠ µ₂

H₀: µ₁ = µ₂
H₁: µ₁ = µ₂

H₀: µ₁ = µ₂
H₁: µ₁ - µ₂ =0

H₀: µ₁ < µ₂
H₁: µ₁ > µ₂

H₀: µ₁ - µ₂ = 1
H₁: µ₁ ≠ µ₂

Açıklama:

For two sided (two tailed) test, the null hypothesis (H₀) and the alternative hypothesis (H₁) are in the following form,
H₀: µ₁ - µ₂ = 0
H₁: µ₁ - µ₂ ≠ 0
This hypothesis equivalently can be expressed as,
H₀: µ₁ = µ₂ (There is no difference)
H₁: µ₁ ≠ µ₂ (There is a difference)
The answer is A.

Doğru Cevap: A

Soru 12

The population variances for two samples are 2 and 5, the difference of the sample means for these two samples is 3, and the sample sizes are 100 and 500, respectively. For the given values what is the test statistic?

Açıklama:

The formula gives the test statistic for two sample tests of means when their population variances are known. since x1 - x2 =3, and the denominator of the formula can be written as {[(2)²/100]+[(5)²/500]}^1/2 which would be equal to 0.3. This would yield to z=3/(0.3) = 10
The answer is A

Doğru Cevap: A

Soru 13

A random sample of 410 from two class in a high school is chosen. 250 of the students is selected from class (A) and their particular subject's mean test score is 70 with a standard deviation of 5. The rest of the students is selected from class (B) and their mean test score is 65 with a standard deviation of 4. At the 1% significance level, can we conclude that class (A) mean test score is better than the class (B)?

Açıklama:

The independent random sample sizes are n_A = 250 students and n_B = 160 students. Also, the class (A) mean test score is x_A = 70 and standard deviation s_A = 5, and the class (B) mean test score is x_B = 65 and standard deviation s_B= 4. Then, the test statistic can be obtained as follows: x_A - x_B = 70 - 65 = 5, s_A² = 25, s_B² = 16. Therefore [(25/250)+(16/160)] = 1/5. The test statistic z=5/(1/5)=25
The answer is B.

Doğru Cevap: B

Soru 14

For sample one the sample size is 10, mean is 4.5, and standard deviation is 1. For sample two the sample size is 12, mean is 3.4, and standard deviation is 1.2 and (µ1 −µ2 ) is considered to be equal to 0. What is the test statistics for the given values?

Açıklama:

Since the sample sizes are smaller than 30 we will use

this formula. The numerator is equal to (4.5 - 3.4) - 0 = 1.1. The denominator is equal to [(1)²/10] +[(1.2)²/12] = 0.1+0.12 = 0.22. these results would yield to a test statistic of z=1.1/0.22 = 5
The answer is B.

Doğru Cevap: B

Soru 15

I. If the alternative hypothesis is in the form of H₁: p1α
II. If the alternative hypothesis is in the form of H₁: p1>p2 then rejection region is z>z_α
II. If the alternative hypothesis is in the form of H₁: p1≠p2 then rejection region is z=z_α/2
For the given statements about the hypothesis test of the difference between two population proportions which ones can be said to be true?

Only I

Only II

I and II

I and III

II and III

Açıklama:

Critical regions for the hypothesis test are summarized below;
If the alternative hypothesis is in the form of H₁: p1≠p2 then rejection region is z>z_α/2 or z <-z_α/2
If the alternative hypothesis is in the form of H₁: p1α
If the alternative hypothesis is in the form of H₁: p1>p2 then rejection region is z>z_α
The answer is C.

Doğru Cevap: C

Soru 16

A chocolate factory is examining the sales of their new brand chocolates in two nearby cities. The number of chocolates sold in city 1 is 300 (n1) and 120 of the chocolates were their new brand chocolates. On the other hand, in the city 2, 240(n2) of the sold chocolates, 150 of them were their new brand chocolates. What is the test statistics? ([(1/300) + (1/240)] can be assumed to be equal to 0.25)

-2.9

-1.9

-1.6

-1.3

-0.9

Açıklama:

n1 =300, x1 = 120 then p1 = x1/n1= 120/300= 0.4
n2 =240, x1 = 150 then p2 = x2/n2= 150/240= 0.625
p = (x1 + x2)/(n1 + n2) = (120 + 150)/(240 + 300) =0.5
Then, z-test is used to test the difference between two proportions p1 and p2 and the test statistic is as follows:

The numarator is 0.4 - 0.625 = -0.225.
0.5x(1-0.5)=0.25, [(1/300)+(1/600)] is assumed to be equal to 0.25 therefore the denominator is 0.25. This yields to z = -0.225/0.25 = -0.9
The answer is E.

Doğru Cevap: E

Soru 17

For the variance between samples equalling 10 and the variance within samples equaling 20, what is the test statistic for a one-way ANOVA test is the ratio of two variances?

0.1

0.2

0.3

Which one of the following is the degrees of freedom for within source of variation in F table?

N-1

N-n

N-k

k-1

k-2

Açıklama:

d.f.D = N - k (N is the total sample size of the groups)

Doğru Cevap: D

Soru 24

Which one of the following is the degrees of freedom for between source of variation in F table?

k-4

k-n

k-N

N-n

k-1

Açıklama:

d.f.N = k - 1 (k stands for the number of groups)

Doğru Cevap: B

Soru 29

What is the shaded region indicated by arrows called in hypothesis testing?

Rejection region

Accept region

Mean region

Variance region

Pearson's r

Açıklama:

Doğru Cevap: A

Soru 30

Which one of the following is an example of null hypothesis for testing the means of two normal distribution?

Mean 1 - Mean 2 = 5

Mean 1 > Mean 2

Mean 1 < Mean 2

Mean 1 - Mean 2 >5

Mean 1 - Mean 2 = 0

Açıklama:

Doğru Cevap: E

Soru 31

In which statistical method, we might write down the following hypothesis:
"Is there any difference for the mean number of defective products which are manufactured by two different machine operators?"

ANOVA

One sample hypothesis testing

Regression analysis

Hypothesis testing for two populations

Kolmogorov-Smirnov

Açıklama:

hypothesis testing problem to two random samples from two different populations to determine whether the population means, or proportions are equal. Some examples for these types of cases are as follows;

Is there any difference for the mean number of defective products which are manufactured by two different machine operators?

Is there any difference of the mean age of customers who are choosing different colours of the same car model?

Is there any difference between the mean exam grade of statistics course taken by economics and management department students?

Is there any difference for the proportion of the student grades which are using two different reference books for the same of course?

Is there any difference for the mean income level of the customers of two different banks?

Doğru Cevap: D

Soru 32

In two population hypothesis testing which of the following is true?

μ1 >5

μ2 < 0

μ1 > ( μ2 - 5)

μ1 - μ2 = -5

μ1 - μ2 = 0

Açıklama:

The null hypothesis can be μ1 - μ2 = 0

Doğru Cevap: E

Soru 33

For the left sided (lower tailed) test for two population means, how do we write the alternate hypothesis?

μ1 - μ2 =0

μ1 > μ2

μ1 < μ2

μ1

μ1 !> μ2

Açıklama:

For the left sided (lower tailed) test, the null hypothesis (H0) and the alternative hypothesis (H1) are in
the following form,
H0: μ1 - μ2 = 0
H1: μ1 - μ2 < 0
This hypothesis equivalently can be expressed as,
H0: μ1 = μ2
H1: μ1 < μ2

Doğru Cevap: C

Soru 34

In a two population hypothesis testing problem, population standard deviations are 40 and 30, sample sizes are 125 and 225 respectively. If the z value is calculated, what is the value of denominator for z?

2.7

6.597

1.879

4.099

2.658

Açıklama:

sqrt(40^2/125 + 30^2 / 225) = 4.099

Doğru Cevap: D

Soru 35

In a two population hypothesis testing problem, the sample arithmetic means are 45 and 80. If the z value is calculated, what is the value of numerator for z?

-15

-25

-35

Açıklama:

the difference is
45 - 80 = -35

Doğru Cevap: C

Soru 36

The independent random sample sizes are n1 = 180 students and n2 =200 students. Also, the sample mean grades are 80 and 90. Population standard deviations are 20 and 40 respectively. What is the z value for the hypothesis testing?

-3.45

-4.59

-7.6

-0.89

-1.82

Açıklama:

(80-90) / sqrt( 20^2/180 + 40^2/200) =-1.82

Doğru Cevap: E

Soru 37

In a two population hypothesis testing problem, the alternate hypothesis sign is not equal and the level of significance 0.05, what is the theoretical value of z from standard normal distribution?

1.88

1.96

2.58

2.33

2.87

Açıklama:

From the standard normal distribution given in the page 79 of your book, the answer is 1.96.

Doğru Cevap: B

Soru 38

The observed z value is 3.62 and theoretical z value is 1.96, then what is the conclusion for hypothesis testing?

Fail to reject null hypothesis

accept null hypothesis

accept the alternate hypothesis

Fail to accept the alternate hypothesis

cant conclude

Açıklama:

Doğru Cevap: C

Soru 39

In a two population hypothesis testing problem, if you draw the normal distribution with critical values, what do we call the inside of the critical values?

H0 rejection region

Shaded region

H1 acceptance region

H0 acceptance region

No region

Açıklama:

Doğru Cevap: D

Soru 40

In a two population proportion problem x1 =50; n1=200; x2=120; n2 =400 then what is the value of joint p value?

0.08

0.12

0.15

0.25

0.28

Açıklama:

(50 + 120) / (200 + 400) =0.28

Doğru Cevap: E

Soru 41

A researcher wants to test whether the average exam scores of two student groups (X and Y respectively) are same or not. How will he/she formulate null hypothesis (H₀) and alternative hypothesis (H₁)?

H₀: X1: X>Y

H₀: Y1: Y>X

H₀: X=Y, H₁: X

H₀: X=Y, H₁: X>Y

H₀: X=Y, H₁: X≠Y

Açıklama:

The null hypothesis is that the average grades are same (X=Y) and the alternative is that they are not same (X≠Y). So the answer is choice E.

Doğru Cevap: E

Soru 42

Which of the following statements is false regarding the test statistic formula below, which is for two sample tests of means when their population variances are known?

x₁-x₂is the difference of the sample mean

The sampling distribution is standard normal distribution.

σ²₁, σ²₂ are known population variances

When any of the sample size is larger than 30, then sample variances could be used instead of population variances.

n₁, n₂ are the sizes of the sample of the two independent populations

Açıklama:

In order to use sample variances instead of population variances, both of the sample sizes must be larger than 30. Thus statement in D is false.

Doğru Cevap: D

Soru 43

A researcher wants to decide whether the average Statistics 101 course exam scores of students of faculty of engineering and faculty of natural sciences are same or not. He takes 60 students from faculty of engineering whose average exam score is 59, and 50 students from faculty of natural sciences whose average score is 65. The variance regarding the exam scores for engineering faculty is 15, and that for natural sciences faculty is 10. What will be the z-statistics for this comparison?

8.94

7.62

6.45

5.63

4.86

Açıklama:

so z=(65-59)/(√15/60+10/50)=6/√0.45=8.94

Doğru Cevap: A

Soru 44

Which of the following problems requires a two-sided test?

Chinese men are taller than the Japanese man.

Meditterian region olives contain more fat than Aegean region olives.

There is no difference between the durations of batteries brand A and brand B.

Mercedes cars are consume produce less carbon monoxit than BMW cars do.

Cancer risk of men is more than that of women.

Açıklama:

Two sided tests are used for deciding the indifference (equality) of two populations Thus answer is C.

Doğru Cevap: C

Soru 45

What is the critical z-value for α=0.05?

1.75

1.96

2.11

2.20

2.33

Açıklama:

If α=0.05, then the area between z=0 and the critical value of z must be (1-0.05)/2=0.4775, which corresponds to z=1.96

Doğru Cevap: B

Soru 46

Which test statistic do we use when the population variances are unkonwn and the sample size is smaller than 30?

z-test

x-test

t-test

y-test

Chi-test

Açıklama:

t-test is used under such circumtances.

Doğru Cevap: C

Soru 47

What will be the degrees of freedom for two samples whose sample sizes are "m" and "n" and if the population variances are assumed to be equal for testing the difference between two means?

The smaller of m and n

m+n-2

m+n-1

m+n

m+n+1

Açıklama:

If population variances are assumed to be equal then the degrees of freedom=m+n-2.

Doğru Cevap: B

Soru 48

Assume that there are two different brands (A and B) producing chocolates. The variance of chocolates are assumed to be different. One chooses 10 chococaltes of brand A and 20 chocolates of brand B and observes that the average weight of brand A sample is 56 gr and brand B is 54 gr. The sample variances for A and B are 1 and 2 gr respectively. What will be the t-statistic and can we conclude that the weights of these brands are different at 0.05 significance level?

t=1.65, weight are same

t=1.81, weights are same

t=2.98, weights are different

t=3.34, weights are same

t=4.47, weights are different

Açıklama:

so t=(56-54)/√(1/10+2/20)=2/√0.2=4.47. Degrees of freedom is 9 (since the smaller of 10-1 and 20-1 is 9) since the population variances are different. Thus the critical value of t=1.833. Since the calculated t is bigger than critical value we reject the null hypothesis that brand A and B have same weight. Thus we conclude that their weights differ at 0.05 significance level.

Doğru Cevap: E

Soru 49

What will be the variance of defect trucks produced by a factory if 10 of every 100 trucks are defect?

0.90

0.45

0.10

0.09

0.01

Açıklama:

Variance=p*(1-p)=0.1*0.9=0.09

Doğru Cevap: D

Soru 50

Which of the following test is used in case of more than two means of population?

Which of the followings represents the population correlation for Pearson’s correlation coefficient?

rho

x‒

Açıklama:

There are two symbols used for Pearson’s correlation coefficient, population correlation is represented by ρ (rho).

Doğru Cevap: B

Soru 5

Which of the following interpretations is true if the negative value is -1 and the positive value is+1 in the interpretation of Pearson’s Correlation Coefficient?

Perfect correlation

Very strong correlation

Strong correlation

Moderate correlation

Weak correlation

Açıklama:

Pearson’s Correlation Coefficient
Perfect correlation

Doğru Cevap: A

Soru 6

Which of the following interpretations is true if the negative value is-0.2 ≥ r > 0.4 in the interpretation of Pearson’s Correlation Coefficient?

Perfect correlation

Very strong correlation

Strong correlation

Moderate correlation

Weak correlation

Açıklama:

Table 5.1 Interpretation of Pearson’s Correlation Coefficient
Weak correlation

Doğru Cevap: E

Soru 7

Which of the followings measures the proportion of the variance of dependent variable (y), given by independent variable (x), when y is expressed as a linear regression on x in correlation and regression problems?

Pearson’s Correlation Coefficient

Coefficient of Determination

Slope of the Regression Line

Simple Linear Regression

Multiple Linear Regression

Açıklama:

In correlation and regression problems, the coefficient of determination measures the proportion of the variance of dependent variable (y), given by independent variable (x), when y is expressed as a linear regression on x. We will study the regression model in the following section.

Doğru Cevap: B

Soru 8

Which of the followings is the process of creating a model of the linear relationship between independent variable and dependent variable ?

Pearson’s Correlation Coefficient

Coefficient of Determination

Slope of the Regression Line

Simple Linear Regression

Multiple Linear Regression

Açıklama:

What is the interpretation of Pearson’s Correlation Coefficient values "-0.8 ≥ r ≥ 0.99"?

Perfect correlation

Very strong correlation

Strong correlation

Moderate correlation

Weak correlation

Açıklama:

Interpretation of Pearson’s Correlation Coefficient

Doğru Cevap: B

Soru 14

What is the interpretation of Pearson’s Correlation Coefficient values "0 < r < 0.2"?

Strong correlation

Moderate correlation

Weak correlation

Very weak correlation

No correlation

Açıklama:

Interpretation of Pearson’s Correlation Coefficient

Doğru Cevap: D

Soru 15

Which of the following statements is true about "H0:ρ=0"?

Correlation cannot be measured

Correlation is insignificant

There is no correlation

There is a correlation

Population correlation is not zero

Açıklama:

H0:ρ=0 (There is no correlation. Population correlation is zero)
H1:ρ≠0 (There is a correlation. Population correlation is not zero)

Doğru Cevap: C

Soru 16

Which of the following is not true about the simple linear regression model

Açıklama:

Doğru Cevap: E

Soru 17

Which of the following is not one of the assumptions in a linear regression model?

The variance of the residuals at all levels of independent variable is not constant

Açıklama:

Doğru Cevap: B

Soru 18

In an investigation, the monthly electricity consumption (kw) of a family of four is estimated by the size of the house (in meter squares). It is going to be a big project, but the investigator creates a pilot study with 10 family homes in a small town. Here are the data values below;

Which of the following is the simple linear regression model for the case above?

Açıklama:

Doğru Cevap: A

Soru 19

What is A in the graph above?

Explained variable

Unexplained variation

Estimate

Observation

Total variation

Açıklama:

Doğru Cevap: D

Soru 20

Which of the following is not true about the multiple linear regression model

the observation parameters

Açıklama:

Doğru Cevap: C

Soru 21

What might be the correlation coefficient according to that graph?

0.65

-0.30

0.20

-0.70

Açıklama:

For detailed information, please review Correlation part at page 101.
As the self-efficacy values increases, achievement values increases too. So, it is called a positive relationship. Secondly, it is obvious that the relationshio is neither perfect nor too weak. So we can say that it is moderate.
So, we can choose the option A since it indicates a positive and moderate relationship.

Doğru Cevap: A

Soru 22

The table given above indicates the correlation coefficients between A, B, C and D variables. According to those correlations, which one of the following statement is wrong?

As the values of A decreases, values of D decreases, too.

The relationship between B-C is stronger than the relationship between B-D.

C and D have a moderate positive relationship.

The weakest relationship is between A and C.

The strongest relationship is between B and C.

Açıklama:

Please review Correlation part at page 101 for detailed information.
The weakest relationship is between B and D.

Doğru Cevap: D

Soru 23

A teacher wants to investigate whether there is a relationship between students' self-efficay and their exam results. 10 students were randomly picked up and their values were recorded and given in the table above. What is the Pearson correlation coefficient between students' self-efficacy scores and their achievement?

0.86

-0.14

0.35

-0.54

0.25

Açıklama:

Please review Page 105 for detailed information.
Pearson Correlation Coefficient formula is given in page 105. You can use and calculate the coefficient as -0.14.

Doğru Cevap: B

Soru 24

If the independent variable explains the 48% of the variability of the dependent variable, what might be the correlation coefficient between this independent and dependent variables?

0.31

0.72

-0.69

0.48

-0.28

Açıklama:

Please review Coefficient of Determination part on page 108.
0.48 is the coefficient of determination. The coefficient of determination is calculated by using the square of Pearson’s correlation coefficient. So if we get the squareroot of it, we can find the correlation coefficient.

Doğru Cevap: C

Soru 25

In a significance test for Pearson correlation coefficient, it is known that the null hypothesis “Population correlation is zero” is rejected. What might be the correlation coefficient? (Number of observation is 10)

0.32

0.45

0.53

0.60

0.69

Açıklama:

Please review the page 109 Significance Test for Pearson’s Correlation Coefficient
t(8;0.05) = 2.306.
If absolute value of the observed t statistics is greater than 2.306, we should reject the Ho.

If we solve the equation, we get 0.63 for the critical r value. The r values less than 0.63 result in an observed t less than 2.306.
So it should be greater than 0.63

Doğru Cevap: E

Soru 26

Assume that the standard deviations of dependent and independent variables are 2.30 and 1.25 respectively. Besides their correlation coefficient is 0.60. What might be the possible regression model for those variables?

Y= 2.30 + 1.25X

Y= 15 + 2.30X

Y= 12 + 0.60X

Y= 10 + 1.10X

Y= 18 + 0.54X

Açıklama:

Please review page 113.

That formula given in page 113 states that, the standart deviations of Y and X and the correlation of them can be used to find the slope of regression equestion. According to our question, the slope is calculated and it is 1.10.
So the only alternative had 1.10 as slope is D.

Doğru Cevap: D

Soru 27

If it is known that the correlation of two variables is -0.49, which of the following statements is true?

As one of the variables decreases, the other one decreases, too.

There is a positive relationship between them.

%49 of the variation of independent varible can be explained by the dependent variable.

%24 of the variation of dependent varible can be explained by the independent variable.

%70 of the variation of independent varible can be explained by the dependent variable.

Açıklama:

Review page 108, Coefficient of Determination part.
The coefficient of determination measures the proportion of the variance of dependent variable (y), given by independent variable (x) and calculated by r^2.

Doğru Cevap: D

Soru 28

Y=5-2.4X
According to the given simple linear regression model, which of the following statement is false?

The one unit change in X results in 2.4 unit change in Y.

As X values increase, Y values decrease.

The constant term of regression equation is 5.

The slope of equation is 2.4.

When X=0, the regression line intersects the Y axis at -2.4.

Açıklama:

Please review the Simple Linear Regression part at page 111.
When X=0, the regression line intersects the Y axis at 5.

Doğru Cevap: E

Soru 29

Y=a + bX
What does b indicates on that regression model?

Slope

Error term

Constant

Average

Intercept

Açıklama:

Please review page 111.
It is slope.

Doğru Cevap: A

Soru 30

A multiple linear regreesion model is given above. Which one of the following statements is correct?

X₁has a negative correlation with Y.

As X₂ increases one unit, Y decreases 0.8 unit.

As X₃ increases one unit, Y decreases 1.2 unit.

The slope of the equation is 15.

There are 2 independent variables at the model.

Açıklama:

Please review page 123, Multiple Linear Regression part.
The answer is B.
There are 3 independent variables at the equation.
X1 and X3 have a positive correlation with Y, while X2 has a negative one.

Doğru Cevap: B

Soru 31

How do you measure the degree of a relationship between two continuous variables?

Correlation

Variance

Mean

Mode

Mc-Nemar

Açıklama:

In general, the correlation analysis looks at the relationship between variables and examines the degree of the relationship if there is any.

Doğru Cevap: A

Soru 32

If the correlation between two variables is 0, which one of the following is true?

There is a correlation

There is a week negative correlation

There is moderate positive correlation

There is a strong negative correlation

There is no correlation

Açıklama:

It means there is no correlation

In a simple linear regression model, the arithmetic mean of the independent variable is 60, arithmetic mean of the dependent variable is 140, and b=1.25. What is the value of "a" for this simple linear regression model?

Açıklama:

a= 140 - 1.25 * 60 =65

Doğru Cevap: D

Soru 40

The estimated simple linear regression model is y= 65 + 2.45 * x, what is the y value according to model if x=12?

71.93

82.83

95.73

102.65

94.40

Açıklama:

y= 65 + 2.45 * 12 = 65 + 29.40 = 94.40

Doğru Cevap: E

Soru 41

In general, the correlation analysis looks at the relationship between variables and examines the degree of the relationship if there is any. Which of following presents the reverse relationship between the values of the variables?

Nonlinear relationship

Positive relationship

Negative relationship

Circular relationship

Pessimistic relationship

Açıklama:

If the change of the values of two variables is synchronised with each other then we have a positive relationship, if there is a reverse relationship between the values of the variables, then we have a negative relationship. The answer is C.

Doğru Cevap: C

Soru 42

It shows the degree of the relationship between two continuous variables
It uses the ρ (rho) symbols.
It gets values between -1 and +1.

Which of the following represents these expressions?

Linear Correlation Analysis

Pearson’s Correlation Coefficient

Regression Analysis

Exponential Coefficient

Slope Analysis

Açıklama:

In order to show the degree of the relationship between two continuous variables, The Pearson’s correlation coefficient or Pearson’s product moment correlation coefficient is widely used. There are two symbols used for Pearson’s correlation coefficient, population correlation is represented by ρ (rho) and sample correlation is represented by r. Pearson’s correlation coefficient gets values between -1 and +1. The answer is B.

Doğru Cevap: B

Soru 43

In a relationship examination between two variables, if the Pearson's coefficient is find as 0.90, which of the following expresses this value?

Between the variables, there is a weak linear relationship

Between the variables, there is no relationship

Between the variables, there is a strong negative relationship

Between the variables, there is a strong positive relationship

Can not be say anything without having the data

Açıklama:

According to the result, there is a very strong relationship between the variables. The answer is D.

Doğru Cevap: D

Soru 44

According to a correlation relationship between two variables, if the coefficient of determination is 0.50, which of the following represents the meaning of this value?

The independent variable in the situation explains half of the variability of the dependent variable.

The independent variable in the situation explains the 7% of the variability of the dependent variable.

There is a moderate linear relationship between the variables.

There is a negative linear relationship between the variables.

The dependent variable in the situation explains the 50% of the variability of the dependent variable.

Açıklama:

The practical meaning of the result can be written as follows: “the independent variable in this problem explains the 50% (half) of the variability of the dependent variable”. The answer is A.

Doğru Cevap: A

Soru 45

In a correlation investigation, if we don't consider the two variables and we are dealing with two different population, which statistical term is come up?

Linearity test for Pearson’s correlation coefficient

Regression test for Pearson’s correlation coefficient

Significance test for Pearson’s correlation coefficient

Test of "r"

Test of "pearson"

Açıklama:

In order to decide if there is a correlation between the population parameters of two continuous variables, we use sample information. We can test the null hypothesis of “population correlation is equal to 0”, or “there is no correlation between two variables” by using sample correlation coefficient. In this case, we will use the t distribution with n-2 degrees of freedom and with a specific significance level (α). In order to use this hypothesis testing, we assume that the underlying distributions of the two variables are Normal distributions. The hypothesis are constituted in the significance test for Pearson’s correlation coefficient. The answer is C.

Doğru Cevap: C

Soru 46

Which of the following represents the amount of variability in the dependent variable that cannot be explained by the linear relationship between independent and dependent variables?

Coefficient of the independent variable

Slope of the regression line

The mean of the dependent variable

Interception of the regression line

Random error ε

Açıklama:

In the model, the random error ε represents the amount of variability in the dependent variable that cannot be explained by the linear relationship between independent and dependent variables. The answer is E.

Doğru Cevap: E

Soru 47

In a simple linear regression model, if the equation is as follow,
y= 5 + (3.5)x
which of following is the mean of the value of "3.5"?

Slope of the regression line

Error value

Intercept of the regression line

The value of "t"

The value of "r"

Açıklama:

y= 5 + (3.5)x,
3.5 is the slope of the regression line. The answer is A.

Doğru Cevap: A

Soru 48

In a simple linear regression model, if the equation is as follow,
y= 5 + (3.5)x
Which of the following can be accepted as a true expression?

There is a positive exponential relationship between the variables

There is a negative relationship between the variables

Without having the data, it can not be say anything.

While "x" increases, "y" increases more.

While "x" increases, "y" will remain at the same value.

Açıklama:

According to the regression equation, while "x" increases, "y" increases more. The answer is D.

Doğru Cevap: D

Soru 49

Which of the following represents the sum of the explained variation and unexplained variation?

Partial variation

Total variation

Related variation

Dependent variable

In The Analysis of Variance Table in Multiple Linear Regression, what is the degrees of freedom if the source of variation is regression?

1-n

k+1

N-1

Açıklama:

Doğru Cevap: C

Soru 54

In The Analysis of Variance Table in Multiple Linear Regression, what is the degrees of freedom if the source of variation is error?

k-1

N-1

N-k-4

n-k-1

Açıklama:

400 / 3

200

Açıklama:

x = (4 / 3) . 100. pg. 140. Correct answer is B.

Doğru Cevap: B

Soru 5

Total price for products group A is 10 and 12 units for months X and Y, respectively. What is the simple aggregate price index for A for month X when month Y is the base?

220

150

500 / 11

250 / 3

Açıklama:

x = (10 / 12) . 100 = 250 / 3.. pg. 142 . Correct answer is D.

Doğru Cevap: D

Soru 6

Total price for products group A is 20 and 18 units for weeks X and Y, respectively. What is the fixed based simple average price index for A for week X when week Y is the base?

100 / 9

100 / 19

Açıklama:

x = (20 / 18) . 100 = 100 / 9. pg. 143. Correct answer is B.

Doğru Cevap: B

Soru 7

Total price and quantity for products group A is 14 and 5, and 25 and 4, as unit a and unit b, for months X and Y, respectively. What is the Laspeyres' price index for A for month X when month Y is the base?

19.5

125 / 7

56.0

70.0

95.0

Açıklama:

x = ((14. 5) / (25 . 4)) . 100 = (70 / 100) . 100 = 70 . pg. 145. Correct answer is D.

Doğru Cevap: D

Soru 8

Total price and quantity for products group A is 5 and 18, and 10 and 20, as unit a and unit b, for years X and Y, respectively. What is the Paasche’s price index for A for year X when year Y is the base?

200

Açıklama:

x = ((5 . 18) / (10 . 20)) . 100 = (90 / 200) . 100 = 45 . pg. 147. Correct answer is B.

Doğru Cevap: B

Soru 9

Total price and quantity for products group A is 4 and 33, and 5 and 40, as unit a and unit b, for years X and Y, respectively. What is the Fisher’s price index for A for year X when year Y is the base?

200.0

132.0

66.0

33.0

16.5

Açıklama:

Fisher's index = (Laspeyres' index . Paashe's index)^1/2 ; for this case : Laspeyres' index . Paashe's index = Fisher's index ; x = ((4 . 33) / (5 . 40)) . 100 = (132 / 200) . 100 = 66 . pg. 149. Correct answer is C.

Doğru Cevap: C

Soru 10

Total price and quantity for products group A is 4 and 50, and 6 and 24, as unit a and unit b, for years X and Y, respectively. What is the Fisher’s price index for A for year Y when year X is the base ?

200

144

125 / 9

Açıklama:

Fisher's index = (Laspeyres' index . Paashe's index)^1/2 ; for this case : Laspeyres' inden . Paashe's index = Fisher's index ; x = ((6 . 24) / (4 . 50)) . 100 = (144 / 200) . 100 = 72 . pg. 149. Correct answer is D.

Doğru Cevap: D

Soru 11

X is 51, Y is 170. What is the simple index number of X compared to Y?

3.33

119

221

442

Açıklama:

x = (51 / 170) . 100 = 30

Doğru Cevap: B

Soru 12

Monthly sales of companies X and Y are 45 units and 72 units, respectively. What is the index for X compared to Y?

1.6

500 / 9

400 / 9

62.5

31.25

Açıklama:

x = (45 / 72) . 100 = 62.5

Doğru Cevap: D

Soru 13

Price of X is 56, and 84 units on February, and May, respectively. January is the base period. What is the fixed based simple price index for May?

150

200 / 3

140

Açıklama:

x = (84 / 56) . 100 = 150

Doğru Cevap: C

Soru 14

Price of X is 4, 8, and 6 units on January, May, and June, respectively. What is the chain-based simple price index for May?

200

200 / 3

Açıklama:

x = (8 / 4) . 100 = 200

Doğru Cevap: A

Soru 15

Total price for products group A is 14 and 16 units for months X and Y, respectively. What is the simple aggregate price index for A for month X when month Y is the base?

224

400 / 3

250 / 7

87.5

Açıklama:

x = (14 / 16) . 100 = 87.5

Doğru Cevap: E

Soru 16

Total price for products group A is 27 and 24 units for weeks X and Y, respectively. What is the fixed based simple average price index for A for week X when week Y is the base?

112.5

100 / 9

100 / 19

Açıklama:

x = (27 / 24) . 100 = 112.5

Doğru Cevap: A

Soru 17

Total price and quantity for products group A is 4 and 15, and 5 and 4, as unit a and unit b, for months X and Y, respectively. What is the Laspeyres' price index for A for month X when month Y is the base?

21.5

140 / 9

64.0

80.0

50.0

Açıklama:

x = ((4 . 15) / (5 . 24)) . 100 = (60 / 120) . 100 = 50

Doğru Cevap: E

Soru 18

Total price and quantity for products group A is 15 and 8, and 25 and 6, as unit a and unit b, for years X and Y, respectively. What is the Paasche’s price index for A for year X when year Y is the base?

250

150

Açıklama:

x = ((15 . 8) / (25 . 6)) . 100 = (120 / 150) . 100 = 80

Doğru Cevap: C

Soru 19

Total price and quantity for products group A is 34 and 3, and 80 and 5, as unit a and unit b, for years X and Y, respectively. What is the Fisher’s price index for A for year X when year Y is the base?

102.0

25.5

400.0

240.0

170.5

Açıklama:

Fisher's index = (Laspeyres' index . Paashe's index)^1/2 ; for this case : Laspeyres' index . Paashe's index = Fisher's index ; x = ((34 . 3) / (80 . 5)) . 100 = (102 / 400) . 100 = 25.5

Doğru Cevap: B

Soru 20

Total price and quantity for products group A is 40 and 8, and 60 and 7, as unit a and unit b, for years X and Y, respectively. What is the Fisher’s price index for A for year Y when year X is the base ?

1400 / 3

1500 / 7

1600 / 21

Açıklama:

Fisher's index = (Laspeyres' index . Paashe's index)^1/2 ; for this case : Laspeyres' inden . Paashe's index = Fisher's index ; x = ((40 . 8) / (60 . 7)) . 100 = (320 / 420) . 100 = 1600 / 21

Doğru Cevap: E

Soru 21

Which of the followings are true definitions about index number?

It measures the relative change
It considers the periods
It is a statistical value
It considers a reference value
It can not transformed an equation

I-II-III

I-II-IV

II-III-V

I-II-III-IV

I-II-III-IV-V

Açıklama:

An index number measures the relative change in price, quantity, value, or some other characteristics of interest compared to a base period. It is a statistical value that measures the change in a variable with respect to the reference value of a variable for a specific period specific period such as a starting year, a specific factory or a specific location. A simple index number can be calculated using the following equation:
Indexnumber = (value/reference value) ×100
The answer is D.

Doğru Cevap: D

Soru 22

For profit situations of some firms compared to firm E, the index numbers are followings;

Firm A - 25
Firm B - 55
Firm C - 130
Firm D - 100

Which of the following presents the ranking of firms from successful to less successful?

C-D-B-A

A-B-D-C

D-C-B-A

A-B-C-D

C-D-A-B

Açıklama:

Since the base is chosen as Firm E, the index value of Firm C is the best. The the ranking is Firm D, Firm B and Firm A. The answer is A.

Doğru Cevap: A

Soru 23

Which of the followings shows the true definition about the fixed base simple index?

Ratio of the value in the current period and value in the fixed base period

Ratio of the value in the fixed base period and value in the current period

Ratio of the value in the fixed base period and value in the period of interest

Ratio of the value in the indexed number and value in the current period

Ratio of the value in the future period and value in the fixed base period

Açıklama:

When you have a fixed period for the calculation of simple index values, all the index values are the division of their current observation values to the base period values of the variable that the index is calculated.
Fixed Base Simple Index = (value in the current period / value in the fixed base period ) * 100

Doğru Cevap: A

Soru 24

Which of the followings presents the importance of the chain based simple index?

It calculates the chain ranking

It permits a comparison between two consecutive periods

It considers the start point in each period

It considers the fixed chain value

It calculates the ratio of the price in the current period

Açıklama:

It is possible that from time to time it is necessary to change the base for an index since many changes may occur as the time goes by. Also, sometimes one might consider the changes between consecutive periods, such as from year to year and week to week. A chain index is an index number where the value of any given period is relative to the value of the preceding period. Remember that in the fixed-base index, the index value of each period in a time series is directly related to the value of a fixed base period. In calculation of a chain-based index, the base period changes from year to year and this permits a comparison between two consecutive periods. The answer is B.

Doğru Cevap: B

Soru 25

The price informations for different products regards to the different years are followings:

According to these information, what is the value of the simple aggregate price index for 2020 by using 2017 as the base period?

0,5

100

200

Açıklama:

The aggregate price for the year of 2017= 12+5+8+5=30
The aggregate price for the year of 2020= 20+15+10+15=60
(60/30)*100= 200
The answer is E.

Doğru Cevap: E

Soru 26

The price informations for different products regards to the different years are followings:

According to these information, what is the simple average price index for 2020 by using 2017 as the base period?

0,5

0,2

2,5

1,2

2,22

Açıklama:

1,66 + 3 + 1,25 + 3 =8,91
8,91 / 4 = 2,22
The answer is E.

Doğru Cevap: E

Soru 27

The following table show the prices and quantities of 4 products. According to the value of the Laspeyres Price index for 2020 using 2015 as the base period, which of the followings shows the correct definition about the price of the product group from 2015 to 2020?

Decreased by %9.31

Increased by %9.31

Increased by %19.36

Decreased by %19.36

Increased by %11.31

Açıklama:

Lp=(((25*100)+(90*80)+(120*150)+(50*50)) / ((30*100)+(60*80)+(100*150)+(50*50))) * 100
= (30200/25300) * 100
=1,1936 * 100
= 119,36
The answer is C.

Doğru Cevap: C

Soru 28

The following table show the prices and quantities of 4 products. According to the value of the Paasche Price index for 2020 using 2015 as the base period, which of the followings shows the correct definition about the price of the product group from 2015 to 2020?

Increased by 46.2%

Increased by 24.2%

Increased by 66%

Decreased by 10%

Same

Açıklama:

Pp=(((25*30)+(90*60)+(120*100)+(50*50)) / ((25*100)+(90*80)+(120*150)+(50*50))) * 100
= (30200/20650) * 100
=1,4624 * 100
= 146,24
The answer is A.

Doğru Cevap: A

Soru 29

What is the geometric mean of the Paasche and Laspeyres indexes?

Geometric index

Multiplied index

Fisher's index

Quantitiy index

Price index

Açıklama:

There are advantages and disadvantages of both Paasche and Laspeyres indexes. In order to compensate, another index was created based on these two indexes. It is called Fisher’s ideal index. It is actually the geometric mean of these two indexes.
The answer is C.

Doğru Cevap: C

Soru 30

If in an index calculation, the quantities of the current period and the prices for both of the current and the base periods are used, which of the followings define this index?

Laspeyres price index

Paasche's price index

Fisher's price index

Fisher's quantity index

Paasche's quanitity index

Açıklama:

The Paasche uses the quantities from the current period rather than a base period therefore it may be said that it reflects the buying habits of today’s customers. Overall, it measures the change in the price of commodities, in terms of quantities related to the current period. The answer is C.

Doğru Cevap: C

Soru 31

An ______________ measures the relative change in price, quantity, value, or some other characteristics of interest compared to a base period?

Average

Mode

Index number

Standard deviation

ANOVA

Açıklama:

An index number measures the relative change in price, quantity, value, or some other characteristics of interest compared to a base period

Doğru Cevap: C

Soru 32

In an index, base value is 50 and today's value is 200, what is the simple index number for today's value?

300

400

500

600

700

Açıklama:

Index number = (200 / 50) * 100=400

Doğru Cevap: B

Soru 33

The following table shows the simple index numbers for a variable. What is the value of the base period.

Açıklama:

The base period will give an index number of 1 and it is obtained for 25.

Doğru Cevap: E

Soru 34

What is the simple index number for Nisan?

2.80

2.40

1.89

3.45

9.6

Açıklama:

simple index number without 100 multiplication
60/25 =2.40

Doğru Cevap: B

Soru 35

What are the simple index numbers for this data set (Jane is base period)?

130.00

150.00

116.67

148.33

166.67

163.33

100.00

120.00

156.67

158.33

186.67

183.33

100.00

150.00

216.67

238.33

446.67

233.33

160.00

350.00

116.67

758.33

466.67

185.33

100.00

150.00

116.67

158.33

166.67

183.33

Açıklama:

Using the formula

Doğru Cevap: E

Soru 36

The price of a product in the base period is 150 TL and the price of the same product in the current period is 200, what is the simple index for price in the current period?

180.65

180.54

150.25

125.50

133.33

Açıklama:

P(n/0)=(200/150)*100

Doğru Cevap: E

Soru 37

If the quantity in the base period is 120 and the quantity in the current period is 100, what is the value of the simple index for quantity for current period?

83.33

75.25

85.1

98.23

Açıklama:

(100 /120)*100 = 83.33

Doğru Cevap: A

Soru 38

What is the chain-based simple index for Dean according to table?

150

110

100

Açıklama:

CBSI=(current/preceding)*100=(220/200)*100=110

Doğru Cevap: C

Soru 39

What is the chain-based simple index for Duke according to table?

15.8

112.87

120.78

82.45

77.78

Açıklama:

CBIP=(current/preceding)*100=(140/180)*100=77.78

Doğru Cevap: E

Soru 40

A ________________ index number is constructed to show the changes when there are a number of different items collected together?

simple

composite

aggregate

average

quantity

Açıklama:

A composite index number is constructed to show the changes when there are a number of different items collected together.

Doğru Cevap: B

Soru 41

Some countries and their populations are given below : Austria:8.751.820 France:65.233.271 Italy: 59.290.969 Spain: 46.397.452 What is the index number for France when compared to Spain?

140.60

127.79

100.00

22.18

18.86

Açıklama:

A simple index number can be calculated using the following equation: I
Indexnumber = (value / referencevalue) ×100
In this example the value is France's population and the reference value is Spain's population.
(65.233.271 / 46.397.452) ×100 = 140.60

Doğru Cevap: A

Soru 42

The manager of a company has looked at the monthly average sales of a product for the last ten years and created the table below :

Choosing January as a base; what is the the simple index number for April?

100

121.71

118.42

263.11

198.23

Açıklama:

Fixed Base Simple Index = (value in the current period / value in the fixed baseperiod) ×100
April Fixed Base Simple Index = (180 / 152) x 100 =118.42

Doğru Cevap: C

Soru 43

Which index indicates the change in the price of a single item between two consecutive periods?

Fixed-Based Simple Index

Chain-Based Simple Index

Simple Index for Quantity

Simple Index for Price

Index Number

Açıklama:

Chain-based simple price index indicates the change in the price of a single item between two consecutive periods. It is calculated by dividing the price of a product in the current period by the price of the same product in the preceding period and the result is expressed as percentage. The correct answer is B.

Doğru Cevap: B

Soru 44

Which index is known as the average of weighted relative prices since it is a composite index number of prices formed by the weighted sum method?

Fisher’s Ideal Index

Paasche's Index

Laspeyres’ Index

Consumer Price Index

Chain-Based Simple Index

Açıklama:

Laspeyres Index was created by the German economist Étienne Laspeyres. The technique designed by Laspeyres uses base-period weights. It consists of the information about the price and quantity of products in different periods. The weighting scheme makes it a better tool than simple indexes. By using the Laspeyres index, it is possible to make a comparison of today’s price and quantity between the price and quantity of items altogether for a base period. The Laspeyres price index is also known as the average of weighted relative prices since it is a composite index number of prices formed by the weighted sum method. The index is found by the ratio of the sum of prices in the current period to the sum of the prices in the base period, these sums are weighted by the respective quantities of the base period. In this case, the weights which are used are the quantities of each commodity in the base period. So, it measures the relative price change of the commodities when the respective quantities are considered unchanged. The correct answer is B.

Doğru Cevap: C

Soru 45

_______is a family of indexes that measures the average change over time in selling prices received by domestic producers of goods and services.
Which of the following completes the definition best?

Consumer Price Index

Producer Price Index

Weighted Composite Indexes

Simple Aggregate Index

Chain-Based Index for Quantity

Açıklama:

The producer price index (PPI) is a family of indexes that measures the average change over time in selling prices received by domestic producers of goods and services. It is an output index and designed for domestic goods’ price changes; imports are not included. This index is based on the first commercial transaction of each product in non-retail markets. The correct answer is B.

Doğru Cevap: B

Soru 46

What is constructed from changes in a number of different items and reflects the average change in the actvity of a group of items from the base period to the period under consideration?

Composite index number

Weighted index number

Index value

Index number

Chain-based index number

Açıklama:

A composite index number is constructed from changes in a number of different items and reflects the average change in the actvity of a group of items from the base period to the period under consideration.The correct answer is A.

Doğru Cevap: A

Soru 47

When are the weighted index numbers used?

When all commodities are of equal importance

When all commodities are not of equal importance

When the commodities are not certain

When the commodities are certain

When the commodities are equal for a year

Açıklama:

When all commodities are not of equal importance in the composite index calculations, weighted index numbers are used by assigning weight to each commodity relative to its importance. The correct answer is B.

Doğru Cevap: B

Doğru Cevap: D

Soru 2

In a binomial test, if the Q is 0.30, what is the value of P?

0.20

0.30

0.50

0.70

0.90

Açıklama:

P = 1 - Q
P = 1 - 0.70
P = 0.70

Doğru Cevap: D

Soru 3

In a binomial test, the investigaor is interested in the proportion of boys in a school. In the sample of 250 students, there are 175 boys. What is the value of P for a binomial test for boys?

0.40

0.50

0.60

0.70

0.80

Açıklama:

P = 175 / 250 = 0.70

Doğru Cevap: D

Soru 4

In a binomial test problem, n = 6 and x = 2, what is the value of

in this problem?

Açıklama:

Answer the following three questions (Q5,Q6 and Q7) according to those information.
The following table contains the exam scores of three different classes.

A mathematics teacher wants to test whether the distribution of exam scores for all classes are identical or not. Which test should be used for that hypothesis testing? (Confidence level= 0.95)

Kruskal-Wallis Test

The Sign Test

Spearman’s Rank Correlation Coefficient

The Chi-Square Goodness of Fit Test

Kolmogorov Smirnov Test

Açıklama:

Review the 'Kruskal Wallis' part at page 178.
There are more than two independent groups in that question. That is why Kruskal Wallis Test should be used.

Doğru Cevap: A

Soru 16

What is the value of test statistic H calculated in that hypothesis testing?

0,424

0,482

0,500

0,625

0,846

Açıklama:

Review the Kruskal Wallis Test at page 178.
Use the H formula at page 178.
H= 0.424

Doğru Cevap: A

Soru 17

What is the decision reached as a result of hypothesis testing process?

Ho is rejected since critical value is greater than the H statistic.

Ho is rejected since critical value is less than the H statistic.

The critical value and H statistic is equal to each other.

Ho is accepted since critical value is less than the H statistic.

Ho is accepted since critical value is greater than the H statistic.

Açıklama:

Review the 'Kruskal Wallis Test'
The critical value is 5.991. The calculated H statistic was 0.424 from the previous question. Since critical value is greater than H statistic, Ho accepted and it is concluded that the exam scores distributions for all departments are identical.

Doğru Cevap: E

Soru 18

I. It is suitable to use when one of the two variables in the question is measured in ordinal scale.
II. Spearman’s Rank Correlation Coefficient is a nonparametric alternative to Pearson.
III. It can be used when association between the variables is not linear.
Which of the statement/s above is correct about Pearson correlation coefficient?

Only I

I and II

Only II

II and III

I, II and III

Açıklama:

Review 'Spearman’s Rank Correlation Coefficient' part.
Pearson’s coefficient of correlation is not suitable if one of the two variables in the
question is measured in ordinal scale or the association between the variables is not linear.

Doğru Cevap: C

Soru 19

Which one of the following values cannot be calculated for Spearman's rank correlation coefficient?

-0.659

-0.325

0.480

0.932

1.25

Açıklama:

Review the 'Spearman Rank Correlation Coefficient' part.
Spearman’s rank correlation coefficient takes the values between -1 and +1.

Doğru Cevap: E

Soru 20

Ho :The distribution of differences is symmetrical around M_D= 0
Which of the following tests is related to the given null hypothesis?

Wilcoxon Signed Rank Test

Kruskal Wallis Test

Binomial Test

The Kolmogorov-Smirnov Test

Spearman’s Rank Correlation Coefficient

Açıklama:

Review the page 175.

Doğru Cevap: A

Soru 21

Which of the following is the correct alternative hypothesis for binomial test?

H1: P ≤ Q

H1: P ~ Q

H1: P = Q

H0: P = Q

H1: P < Q

Açıklama:

Two different approaches in the binomial test can be used since the test statistics used in the binomial test change according to sample size. These approaches are called the small sample and the large sample approaches. If the sample size is n ≤ 25, we accept the sample size is small, otherwise the sample size is accepted as large In the binomial test, alternative hypotheses are constructed in three different ways. The hypotheses can be written as follows.
H1:P < Q
H1:P > Q
H1:P ≠ Q

Doğru Cevap: E

Soru 22

..................... is a measure of association for ranked data. In addition, it can be used when the relation between two variables is not linear.
Which of the following test is described above?

Spearman’s rank correlation coefficient

Wilcoxon rank sum test

The Binomial Test

One-Sample Test

Goodness of Fit Test

Açıklama:

Of all the statistical techniques involving ranks, Spearman’s rank correlation coefficient is the earliest one and today it is well known among the scientists. Spearman’s rank correlation coefficient is a measure of association for ranked data. In addition, it can be used when the relation between two variables is not linear.

Doğru Cevap: A

Soru 23

.........................is a non-parametric alternative test for one sample t test, paired sample t test, and a researchin which quantitative measurements is impossible but in which it is possible to rank the measurements with respect to each other. It is used for the hypothesis test about the population median, M. Inferences about the population median are important when the population has highly skewed distribution. Which of the following test should be writen to the gap?

One-Sample Test

Goodness of Fit Test

The Binomial Test

The Sign Test

Wilcoxon Rank Sum Test

Açıklama:

The sign test gets its name from the negative and positive signs of the mathematical difference of the observations’ measurements. It is used for the hypothesis test about the population median, M. Inferences about the population median are important when the population has highly skewed distribution. In skewed distributions, the population median is more centrally located than the population mean. Therefore, population median is accepted as better estimator for the measure of location if the population is skewed. The sign test is a non-parametric alternative test for one sample t test, paired sample t test, and a research in which quantitative measurements is impossible but in which it is possible to rank the measurements with respect to each other.

Doğru Cevap: D

Soru 24

Which of the following test is the most commonly used goodness of fit test?

The Chi-Square Test

The Kolmogorov-Smirnov Test

Wilcoxon Rank Sum Test

Wilcoxon Signed Rank Test

Kruskal-Wallis Test

Açıklama:

The functional form of a population distribution is often needed when performing statistical analyses. The functional form of the distribution may be used for confirming a theory or validating a statistical model which
is used to analyze the data. Goodness of fit tests are used to determine whether a data set comes from a particular distribution.
Some null and alternative hypotheses examples about the population distributions are given below.

H0 : The population distribution is Normal Distribution
H1 : The population distribution is not Normal Distribution
H0 : The population distribution is Poisson Distributio
H1 : The population distribution is not Poisson Distribution

The most commonly used goodness of fit test is the chi-square goodness of fit test.

Doğru Cevap: A

Soru 25

Which of the following non-parametric tests is not used for one-sample-problem?

Spearman’s Rank Correlation Coefficient

The Kolmogorov-Smirnov Test

The Chi-Square Goodness of Fit Test

The Sign Test

The Binomial Test

Açıklama:

Generally, there are four non-parametric tests for one sample case. These are:

The Binomial Test

The SignTest

The Chi-Square Goodness of Fit Test

The Kolmogorov-Smirnov Test

Doğru Cevap: A

Soru 26

I. H1 : The first population is shifted to the right of the second population
II. H1 : The first population is shifted to the left of the second population
III. H1 : The first and the second populations are shifted from each other
Which of the above is the correct alternative hypothesis sentence for Wilcoxon Rank Sum Test?

III

II, III

I, II, III

Açıklama:

H0 : The two populations are identical
H1a : The first population is shifted to the right of the second population
H1b : The first population is shifted to the left of the second population
H1c : The first and the second populations are shifted from each other

Doğru Cevap: E

Soru 27

What is the value ranged of Spearman’s Rank Correlation Coefficient?

-1,0

-0,1, 0

0, +1

0, +0,1

-1 , + 1

Açıklama:

Spearman’s rank correlation coefficient takes the values between -1 and +1. The coefficient close to +1 indicates positive association between the variables. On the other hand, negative values close to -1 denotes negativeassociation. A value near 0 means there is no association between these two variables.

Doğru Cevap: E

Soru 28

Which of the following is non-parametric statistics for two dependent samples?

Wilcoxon Rank Sum Test

Wilcoxon Signed Rank Test

Kruskal-Wallis Test

The Kolmogorov-Smirnov Test

Spearman Rank Correlation Coefficient

Açıklama:

When we consider that the population of differences are symmetrical, a non-parametric test, which is called Wilcoxon signed rank, test is often more powerful than the sign test for making inferences about the population median differences MD. Hence, the main assumption of the test is that the population of differences are continuous and symmetrical.
Specifically, the test under consideration is called Wilcoxon Signed Rank Test for use in a design where there are twodependent populations.

Doğru Cevap: B

Soru 29

............ is used to decide whether k independent samples are drawn from different populations. It is an extension of the Wilcoxon sum rank test to a comparison of more than two populations. It assumes that the variable under consideration is measured on at least ordinal scale.
Which of the following test should be written the gap above.

Kruskal-Wallis Test

Spearman’s Rank Correlation Coefficient

Wilcoxon Signed Rank Test

The Kolmogorov-Smirnov Test

The Chi-Square Goodness of Fit Test

Açıklama:

The one-way analysis of variance has some assumptions such as independent samples, normality, and equal variances. When the conditions of normality and equal variances are not valid, Kruskal-Wallis is a non-parametric alternative test that involves less conditions. The Kruskal-Wallis test is used to decide whether k independent samples are drawn from different populations. It is an extension of the Wilcoxon sum rank test to a comparison of more than two populations. The Kruskal-Wallis test assumes that the variable under consideration is measured on at least ordinal scale.

Doğru Cevap: A

Soru 30

What does the value near 0 of Spearman’s rank correlation coefficient mean?

Negative association between the variables

Positive association between the variables

No association between these two variables.

Very few association between these two variables.

These two variables follow follow same patern.

Açıklama:

Spearman’s rank correlation coefficient takes the values between -1 and +1. The coefficient close to +1 indicates positive association between the variables. On the other hand, negative values close to -1 denotes negative association. A value near 0 means there is no association between these two variables.

Doğru Cevap: C

Soru 31

If the assumptions of certain tests can not be satisfied what do we need to use for testing?

ANOVA

Linear Regression

Non-Parametric statistics

Parametric statistics

Variance

Açıklama:

Parametric tests used in statistics require to specify certain conditions or assumptions to be met in order to make decisions and estimates about population parameters using sample data. The reliability of a parametric test depends heavily on the validity of the assumptions. In addition, parametric tests require at least interval scaled measurements. As you can easily imagine that restricting the data measurement level to interval scales creates a problem since the world, we live in, is not just surrounded by variables that are measured in interval scale.
A non-parametric statistical test does not specify certain conditions or assumptions to be met about population parameters using sample data. The assumptions used in non-parametric tests are that the observations in the sample are independent and the variable under study has underlying continuity. However, these assumptions are fewer and weaker than those used in parametric tests.

Doğru Cevap: C

Soru 32

When a probability of obtaining an outcome, out of two outcomes, on one trial is known and a probability of the number of times the same outcome might appear, say x times out of n independent trials is tried to be found, which probability distribution is used?

Normal

Binomial

Açıklama:

There is a specific distribution called binomial distribution. The Binomial distribution is used when a probability of obtaining an outcome, out of two outcomes, on one trial is known and a probability of the number of times the same outcome might appear, say x times out of n independent trials is tried to be found. Mainly the binomial distribution is the sampling distribution of the proportions estimated from sample data. The binomial test tells us whether it is reasonable to conclude that the proportions we obtain from our sample could have been drawn from a population with a particular value of P.

Doğru Cevap: E

Soru 33

If the alternative hypothesis is written as H1:P < Q in small sample Binomial test, how do we find the p-value?

Açıklama:

Doğru Cevap: A

Soru 34

________________ tests are used to determine whether a data set comes from a particular distribution?

t-test

z-test

Goodness of fit tests

ANOVA

Regression

Açıklama:

Goodness of fit tests are used to determine whether a data set comes from a particular distribution.

Doğru Cevap: C

Soru 35

In a Chi-square goodness of fit test, the observed value is 85, the expected value of the same observation is 80, what is the contribution of these values to overall chi-square value?

0.1258

0.6578

0.3125

0.4545

0.1595

Açıklama:

single observation contribution is
(85 -80)^2 / 80 = 0.3125

Doğru Cevap: C

Soru 36

If the Chi-Square goodness of fit test is applied to data in the table, what is the total chi-square value?

32.56

38.98

30.83

45.12

65.78

Açıklama:

Doğru Cevap: C

Soru 37

If the degrees of freedom is 10 and right tale area is 0.10, what is the chi-square value from the chi-square table?

15.987

14.684

17.275

17.535

16.750

Açıklama:

You need to use the table 7.3 in page 167 of your course book.

Doğru Cevap: A

Soru 38

What is the non-parametric alternative of t test?

ANOVA

Chi-Square

Mann-Whitney dependence

Wilcoxon Rank Sum Test

Binomial

Açıklama:

The parametric independent samples t test is based on several assumptions: two samples are independent of each other, the populations in the investigation for t test are normally distributed, and two populations that these two samples are taken from has the same variability. The Wilcoxon rank sum test is a non- parametric alternative test that involves less assumptions. Especially it does not require that our two populations have a specific known distribution. As long as the populations in question are independent and has the same variability, you may use Wilcoxon Rank Sum test. Therefore, if you want to know if two samples come from independent populations, this method is a good choice. Wilcoxon rank sum test assumes that the two population distributions are identical, although they may differ in location parameter, such as one distribution may be shifted to the right or to the left of the other distribution.

Doğru Cevap: D

Soru 39

In Wilcoxon Rank Sum Test n₁=45 and n₂=40 then what is the value of E[S]?

2000

1935

1800

1725

1635

Açıklama:

E(S)=(45*(45+40+1))/2=1935

Doğru Cevap: B

Soru 40

In Wilcoxon Signed Rank Test if n=25 then what is the value of E[S]?

185.50

162.50

142.50

132.50

122.50

Açıklama:

25*(25+1)/4=162.50

Doğru Cevap: B

Soru 41

If we know the proportion P for one class, the proportion of Q for the other class must be equal to which of the following below?

1-P

1-Q

Q-P

1+P

1+Q

Açıklama:

You may have noticed that the outcomes of some variables are restricted to two outcomes such as male-female, clean-dirty, and broken-not broken etc. If you carefully study the environment we live in, you may see that sometimes populations consist of only two categories/classes or two subpopulations. For example, as we said before, such classes are male and female, dead and alive, married and not married. The population proportions of two categories/classes are denoted by, in general, P and Q. If we know the proportion P for one class, the proportion of Q for the other class must be equal to 1 - P. Because the total probability must be equal to 1 and there are only two possible outcomes. The correct answer is A.

Doğru Cevap: A

Soru 42

If the proportion of married people in a group is 0.63, what is the proportion of single people in the group?

0.17

0.27

0.37

0.50

0.63

Açıklama:

If we know the proportion P for one class, the proportion of Q for the other class must be equal to 1 - P. Because the total probability must be equal to 1 and there are only two possible outcomes. For example, if the proportion of married people in a group is P = 0.63 then the proportion of the single in that group is Q=1-P = 1- 0.63 = 0.37. The correct answer is C.

Doğru Cevap: C

Which test is used to decide whether k independent samples are drawn from different populations?

The Sign Test

Kruskal-Wallis Test

The Wilcoxon Rank Sum Test

The Wilcoxon Signed Rank Test

Spearman Rank Correlation Coefficient

Açıklama:

Doğru Cevap: B

Soru 48

The table shows s the times (in minutes) spent by five students revising for a test and the grades that they achieved in the test. What is Spearman’s rank correlation coefficient?

0.1

0.2

0.3

0.5

Açıklama:

Doğru Cevap: C

Soru 49

Which of the following can be writen as a null hypothesis for The Chi-square Goodness of Fit Test?

The population distribution is normal distribution.

The population distribution is uniform.

Distribution for duration of service is uniform distribution.

The two populations are identical.

The distribution of differences is symmetrical around MD = 0.

Açıklama:

Goodness of fit tests are used to determine whether a data set comes from a particular distribution. Some null and alternative hypotheses examples about the population distributions are given below.
H0 : The population distribution is Normal Distribution
H1 : The population distribution is not Normal Distribution
H0 : The population distribution is Poisson Distribution
H1 : The population distribution is not Poisson Distribution
The correct answer is A.

Doğru Cevap: A

Soru 50

The number of thefts occurring in each season (winter, spring, summer, fall) in a province for the last year is given below:
Winter: 15
Spring: 25
Summer: 80
Fall: 70
What is the expected probability according to uniform distribution?

0.25

-0.2

-0.6

-0.7

-0.8

-0.9

Açıklama:

x = max = -0.2 . If the payoff table is based on costs, first for each decision alternative, the maximum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative. pg. 190. Correct answer is A.

Doğru Cevap: A

Soru 5

The payoff values for decision alternatives : there are 5 states of nature and minimum payoff values for 5 decision alternatives are I) 11.650, II) 10.025, III) 5.275, IV) 2.725, V) 3.450. The decision maker is pessimistic. Which decision alternative is choosen?

III

If Wi stands for the weather type and Vi stands for the vehicle choosen by Ahmet to go to work, how will his payoff matrix would look like?

Sunny (W1)	Rainy (W2)	Snowy (W3)
By Car(V1)	10	15	20
By Bus(V2)	20	25	35

Sunny (W1)	Rainy (W2)	Snowy (W3)
By Car(V1)	15	15	20
By Bus(V2)	20	30	35

Sunny (W1)	Rainy (W2)	Snowy (W3)
By Car(V1)	20	25	20
By Bus(V2)	10	35	35

Sunny (W1)	Rainy (W2)	Snowy (W3)
By Car(V1)	15	25	35
By Bus(V2)	20	25	45

Sunny (W1)	Rainy (W2)	Snowy (W3)
By Car(V1)	10	20	30
By Bus(V2)	15	25	35

Açıklama:

The correct payoff matrix which show different duration of going to work under different weather conditions and with different alternatives of vehicles is shown in A.

Doğru Cevap: A

Soru 15

Under this optimistic criterion, the decision maker calculates the best possible payoff for each decision alternative (among all possible states of nature, for that specific alternative), and then he/she chooses the decision that has the maximum best possible outcome. Which criterion is this?

Minimax

Maximin

Maximax

Minimin

Optimum

Açıklama:

It is the maximax criterion because the decision maker chooses the maximum payoff value for each alternative and selects the action which provides highest of these.

Doğru Cevap: C

Soru 16

According to which criterion a decision maker choose that course of action which minimizes the minimum possible pay - offs?

Minimax

Maximin

Maximax

Minimin

Optimum

Açıklama:

The defined criterion is the minimin, which suggests to choose the action with possible minimum payoff.

Doğru Cevap: D

Soru 17

Answer the questions 7-8 according to following information.
A company has 5 different alternative actions denoted by A1, A2,..A5 under 3 possible states of nature, which are denoted by S1, S2 and S3. The pay off matrix for each action and state of nature is given as:

What will be the best action under maximax criterion?

Açıklama:

maxA1=max(7,10,8)=10
maxA2=max(9,7,12)=12
maxA3=max(14,13,11)=14*
maxA4=max(9,8,6)=9
maxA5=max(7,4,5)=7
Thus A3 gives the maximum of maximum possible payoffs.

Doğru Cevap: C

Soru 18

What would be the best action under minimin criterion?

Açıklama:

MinA1=min(7,10,8)=7
MinA2=min(9,7,12)=7
MinA3=min(14,13,11)=11
MinA4=min(9,8,6)=6
MinA5=min(7,4,5)=4
Thus action 5 gives the minimum of the minimum possible payoffs.

Doğru Cevap: E

Soru 19

In which criterion a level of optimism (alpha) is attained for the maximum value of each action, 1-alpha to minimum value and then a weighted average payoff is calculated?

Hurwicz's

Wald's

Plunger's

Shorrock's

Tucker's

Açıklama:

It's the Hurwic's criterion. The average payoff=α *Max+(1-α )Min

Doğru Cevap: A

Soru 20

For a company, 3 different states of nature are given as S1, S2 and S3 with possibilities 0.4, 0.5 and 0.1 respectively. The alternative actions on the other hand are given as A1, A2, and A3. What will be the best action provides the highest expected payoff and what will be the expected payoff given that action is taken; if the payoff matrix is given as:

A1, with expected pay off=44

A2, with expected pay-off=67

A2, with expected pay-off=57

A3, with expected pay-off=70

A3, with expected pay-off=57

Açıklama:

Action A2 gives the maximum expected pay off which is equal to 60*0.4+70*0.5+80*0.1=67. The expected pay offs of A1 and A3 are 44 and 57 respectively.

Doğru Cevap: B

Soru 21

Which of the followings is the first step in decision making process?

Finding out about the “states of world”, or “states of nature”.

Investigating about the alternatives to solve the decision problem.

Defining the decision problem.

Calculating a payoff value.

Creating payoff matrix or decision table.

Açıklama:

COMPONENTS OF DECISION PROBLEM
The first step is to define the decision problem. We need to clearly identify our decision problem and study all the characteristic of the decision problem. We should ensure that when the decision problem is laid out everyone should understand the same think. There should be no debatable points on what the extend of the decision problem is and what is the size of the decision problem etc.

Doğru Cevap: C

Soru 22

In which of the following decision making environment, the decision maker can list all the states of nature that are possible in the decision problem but cannot assign any probability value to the specific state of nature that might happen?

Decision making under certainty

Decision making under uncertainty

Decision making under risk

Decision making under stress

Decision making under control

Açıklama:

COMPONENTS OF DECISION PROBLEM
The second decision making environment is decision making under uncertainty. In this environment, the decision maker can list all the states of nature that are possible in the decision problem but cannot assign any probability value to the specific state of nature that might happen.

Doğru Cevap: B

Soru 23

In which of the following decision making environment, the decision maker is able to assign probabilities to states of nature?

Decision making under certainty

Decision making under uncertainty

Decision making under risk

Decision making under stress

Decision making under control

Açıklama:

COMPONENTS OF DECISION PROBLEM
The last decision making environment is decision making under risk. In this setting the decision maker is able to assign probabilities to states of nature. In this environment, decision maker assigns a probability to each state of nature, therefore decision maker is able to calculate how much risk is taken if that state of nature happens.

Doğru Cevap: C

Soru 24

In which of the following approaches; decision maker creates the payoff table based on either profit or cost for each combination of decision alternative and state of nature, chooses the maximum or minimum payoff value for each decision alternative, and selects the decision alternative that gives the highest or lowest of these payoffs.

Optimistic Approach

Pessimistic Approach

The Hurwicz Criterion

Expected Monetary Value

Decision Tree

Açıklama:

DECISION MAKING UNDER UNCERTAINITY
As the name implies, in optimistic approach, decision maker thinks that all the good things will happen. Decision maker creates the payoff table based on either profit or cost for each combination of decision alternative and state of nature. Then, the decision maker chooses the maximum or minimum payoff value for each decision alternative, and then decision maker selects the decision alternative that gives the highest or lowest of these payoffs. This method is also known as Plunger’s optimism criterion.

Doğru Cevap: A

Soru 25

Which of the followings happen if the payoff matrix is based on costs?

First the maximum payoff value of each decision alternative is found then among these payoff values, the decision alternative producing the maximum is chosen as the best decision alternative.

First the minimum payoff value of each decision alternative is found then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative.

Decision maker creates the payoff matrix using the cost values that might be realised for each combination of decision alternative and state of nature.

First for each decision alternative, the minimum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the maximum is chosen as the best decision alternative.

first for each decision alternative, the maximum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative.

Açıklama:

Maximin and Minimax Criterions (Pessimistic Approach)
If the payoff matrix is based on costs, first the minimum payoff value of each decision alternative is found then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative.

Doğru Cevap: B

Soru 26

Which of the followings will show you all the possible decision alternatives of the problem, all the states of nature and the payoff values for each of alternative and states of nature combination as a manager in a company and want to invest/build a new factory?

Payoff Matrix

Decision Tree

Decision Node

Chance Node

End Node

Açıklama:

Constructing payoff matrix
If you are a manager in a company and want to invest/build a new factory, there are many parameters to think about. There are also different conditions that will affect the result of your decision alternative. The payoff matrix will show you all the possible decision alternatives of the problem, all the states of nature and the payoff values for each of alternative and states of nature combination.

Doğru Cevap: A

Soru 27

Which of the following statements is not true regarding decision making?

The decision maker lists all the possible decision alternatives and also knows all the possible states of nature that may be realized in decision making problem.

Decision maker studies the problem extensively to be ale to find the states of nature the states of nature that can be seen in the decision-making process.

Decision maker knows what the states of nature are in the decision problem and able to assign a probability value to any of states of nature.

There are decision alternatives and states of nature, but we don’t know which state of nature really might happen and even we cannot put a probability to any of the states of nature that might happen in the future.

There are different approaches to solve the decision making problems.

Açıklama:

Making a decision under uncertainty
Decision maker knows what the states of nature are in the decision problem but not able to assign a probability value to any of states of nature.

Doğru Cevap: C

Soru 28

Which of the following statements is not true regarding making a decision?

We are able to assign any probability of occurrence to any of the states of nature.

There is a complete uncertainty for the decision maker.

When the decision maker is faced with a decision with two or more decision alternatives, decision maker starts to investigate the components of the decision problem.

If the decision maker is able to assign the probabilities to states of nature, then it is said that the decision is made under the risk environment.

Decision maker usually looks at the past data to assign the probabilities to the states of nature.

Açıklama:

Making a decision under risk
We are not able to assign any probability of occurrence to any of the states of nature.

Doğru Cevap: A

Soru 29

Which of the following consequences most probably occurs if the probability values are obtained from an outside firm?

The payoff matrix will show you all the possible decision alternatives of the problem.

The amount of money spent on the process should be incorporated into the payoff matrix calculations.

Branches of the chance nodes of the decision tree of the decision problem do not include the probabilities.

A chance node might be followed by a decision node.

The appropriate payoff value is written.

Açıklama:

Making a decision under risk
If the probability values are obtained from an outside firm, then the amount of money spent on the process should be incorporated into the payoff matrix calculations.

Doğru Cevap: B

Soru 30

Which of the followings happen once the path is identified, from the payoff matrix?

The maximum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative.

The decision alternative producing the maximum of the expected values is chosen as the best decision alternative.

The decision alternative producing the minimum of the expected values is chosen as the best decision alternative

The interpretation of the decision tree gets complicated.

The appropriate payoff value is written.

Açıklama:

Decision Tree
End node: end note is represented with vertical line ( | ). Next to the end nodes, the payoff values are written. The payoff value to be written is found by following the path from the main decision node to the end node. Once the path is identified, from the payoff matrix, the appropriate payoff value is written.

Doğru Cevap: E

Soru 31

The payoff values for decision alternatives : there are 6 states of nature and the profit values for the first decision alternative are 690, 780, 540, 410, 710, 320. The decision maker is optimistic. Which payoff value is taken from the first decision alternative?

410

540

710

780

320

Açıklama:

x = max = 780. pg. 190. Correct answer is D.

Doğru Cevap: D

Soru 32

The payoff values for decision alternatives : there are 6 states of nature and the cost values for the first decision alternative are 960, 710, 450, 610, 430, 580. The decision maker is optimistic. Which payoff value is taken from the first decision alternative?

610

710

450

960

430

Açıklama:

x = min = 430 . pg. 190. Correct answer is E.

Doğru Cevap: E

Soru 33

The payoff values for decision alternatives : there are 6 states of nature and the profit values for the first decision alternative are 550, 720, 410, 190, 780, 260. The decision maker is pessimistic. Which payoff value is taken from the first decision alternative?

550

260

780

190

720

Açıklama:

x = min = 190. If the payoff table is based on profits, first for each decision alternative, the minimum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the maximum is chosen as the best decision alternative. pg. 190. Correct answer is D.

Doğru Cevap: D

Soru 34

The payoff values for decision alternatives : there are 6 states of nature and the cost values for the first decision alternative are -0.75, -0.85, -0.15, -0.65, -0.55, -0.05. The decision maker is pessimistic. Which payoff value is taken from the first decision alternative?

-0.15

-0.55

-0.75

-0.85

-0.05

Açıklama:

x = max = -0.05 . If the payoff table is based on costs, first for each decision alternative, the maximum payoff value of each decision alternative is listed then among these payoff values the decision alternative producing the minimum is chosen as the best decision alternative. pg. 190. Correct answer is E.

Doğru Cevap: E

Soru 35

The payoff values for decision alternatives : there are 5 states of nature and minimum payoff values for 6 decision alternatives are I) 61.150, II) 90.125, III) 20.575, IV) 70.225, V) 40.350, VI) 14.750. The decision maker is pessimistic. Which decision alternative is choosen?

The payoff values for decision alternatives : there are 5 states of nature and minimum payoff values for 5 decision alternatives are I) 1.150, II) 1.025, III) 1.275, IV) 1.725, V) 1.450. The decision maker is pessimistic. Which decision alternative is choosen?

III

A decision alternative has 80 and 30 as payoff values and the probabilities of the associated states of nature are 0.60 and 0.40 respectively. What is the expected monetary value of this decision alternative?

Açıklama:

x = 80 . 0.6 + 30 . 04 = 48 + 12 = 60 . pg. 197 . Correct answer is B.

Doğru Cevap: B

Soru 51

In decision making, _____________ are the outcomes on which the decision maker has little or no control.

probability

data

payoff matrix

states of nature

payoff

Açıklama:

In decision making, states of nature are the outcomes on which the decision maker has little or no control.

Doğru Cevap: D

Soru 52

In decision making, for each combination of decision alternative and state of nature, a ____________ value is calculated?

probability

mean

mode

alternative

payoff

Açıklama:

For each combination of decision alternative and state of nature, a payoff value is calculated.

Doğru Cevap: E

Soru 53

In decision making, at least how many decision alternatives are necessary?

Açıklama:

Once the problem is clearly defined, the next logical step is to investigate about the alternatives to solve the decision problem. We should find all the possible alternatives for the solution of the decision problem.

Doğru Cevap: B

Soru 54

In decision making, where do we show all the possible decision alternatives of the problem, all the states of nature and the payoff values for each of alternative and states of nature combination?

ANOVA table

t table

Identitiy matrix

Payoff matrix

Mode and median

Açıklama:

Once all the payoff values are calculated, a payoff matrix or decision table is created. The payoff matrix will show you all the possible decision alternatives of the problem, all the states of nature and the payoff values for each of alternative and states of nature combination.

Doğru Cevap: D

Soru 55

What is the value of maximax criterion for this profit based payoff matrix?

100

Açıklama:

Doğru Cevap: D

Soru 56

What is the value of minimin criterion for this profit based payoff matrix?

Açıklama:

Doğru Cevap: A

Soru 57

In which decision making criterion The decision maker tries to minimize the damage since the overall approach is to look for the best among the worst payoff values?

maximax

minimin

Maximin

Max

probabilistic

Açıklama:

This method is also known as Wald’s pessimism criterion. In here, the decision maker follows a pessimistic approach to solve the decision problem. The decision maker tries to minimize the damage since the overall approach is to look for the best among the worst payoff values. Decision maker creates the payoff table table either profit or cost based for each combination of (decision alternative, state of nature). Then, the decision maker chooses the minimum or maximum payoff value for each decision alternative, and then decision maker selects the decision alternative that gives the lowest or highest of these payoffs.

Doğru Cevap: C

Soru 58

In Hurwicz criterion, if the value of coefficient of optimism is equal to 1, what is the state of the mind of decision maker?

Pessimistic

Realistic

Doubtful

Optimistic

Cost effective

Açıklama:

In a paper in 1951, Leonard Hurwicz suggested a new method that balances the optimism and pessimism of the decision maker. In this method, the decision maker is allowed to have best and worst possible outcomes considered. In order to achieve this, Hurwicz suggests the use of coefficient of optimism. It is symbolized with α and it is a decimal number between 0 and 1. If α = 1, then the decision maker is hundred percent optimistic. If α = 0, then the decision maker is hundred percent pessimistic. Since α is the level of optimism we may easily call 1 - α as the level of pessimism in the decision problem. Therefore, by changing the value of the α, the decision maker may try to balance the optimism and pessimism.

Doğru Cevap: D

Soru 59

What is the expected monetary value of this profit based payoff matrix?

200.45

225.70

251.65

300.25

350.45

Açıklama:

Doğru Cevap: C

Soru 60

What is the expected monetary value of the decision alternative A3?

65.12

78.6

102.9

114.2

84.80

Açıklama:

Doğru Cevap: E

Statıstıcs II (ENG) - Tüm Sorular

Ünite 1

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Ünite 2

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