Deck 7: Probability and Sampling Distributions

Question 1

The shape of the sampling distribution of the mean is approximately ______,whereas the shape of the sampling distribution of the variance is approximately ______.

A) normal; normal
B) positively skewed; normal
C) normal; positively skewed
D) positively skewed; positively skewed

Answer 1

normal; positively skewed

Question 2

A researcher selects from a participant pool of four males and six females.He determines that the probability of selecting two male participants is p = .16.Based on this probability,what strategy did the researcher use to sample participants?

A) sampling with replacement
B) sampling without replacement

Answer 2

sampling with replacement

Question 3

What values are distributed along the x-axis for a sampling distribution of the sample variance?

A) scores
B) sample means
C) sample variances
D) sample means and sample variances

Answer 3

sample variances

Question 4

In terms of characterizing samples,statistical theory was developed using a sampling strategy in which

A) the order of selecting participants matters.
B) the same participant can be selected twice in the same sample.
C) participants are replaced after being sampled.
D) all of these.

Question 5

A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23.Based on the characteristics of the sample mean,what does this say about the mean in the population?

A) Nothing; it was just a sample.
B) There is no way to know without knowing the size of the sample.
C) It tells us that the mean in the population is no less than 23.
D) We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.

Question 6

A researcher selects a sample of size 4 from a population of size 6.How many possible samples of this size can be selected using experimental sampling?

A) 15
B) 30
C) 1,296
D) 4,096

Question 7

A sampling distribution of the sample mean or variance is

A) a distribution of all measures that could be obtained in a given sample of a given size.
B) a distribution of all scores that could be obtained in samples of a given size from one or more populations.
C) a distribution of all scores that could be obtained in a population.
D) a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population.

Question 8

A researcher selects from a participant pool of four males and six females.He determines that the probability of selecting two female participants is p = .30.Based on this probability,what strategy did the researcher use to sample participants?

A) sampling with replacement
B) sampling without replacement

Question 9

Which type of sampling is most often applied by researchers in the behavioral sciences?

A) theoretical sampling
B) normal sampling
C) experimental sampling
D) standard normal sampling

Question 10

A researcher randomly selects a sample of participants from a population with a variance of 4.If the researcher selects a sample of 16 participants with a mean of 12,then what is the mean and standard error for the sampling distribution of the mean?

A) mean = 12, standard error = 2
B) mean = 12, standard error = 1
C) mean = 12, standard error = 0.5
D) There is not enough information to answer this question.

Question 11

It happens to be the case that the standard error of the sampling distribution of sample means

A) is minimal.
B) is approximately equal to that in the population.
C) gets larger as the sample size increases.
D) is minimal and gets larger as the sample size increases.

Question 12

Regardless of the distribution of the population,the sampling distribution of sample means will be approximately normally distributed.What characteristic of the mean explains this?

A) unbiased estimator
B) central limit theorem
C) minimal variance
D) none of these

Question 13

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called

A) a conditional procedure.
B) a sampling distribution.
C) sampling without replacement.
D) random sampling.

Question 14

What values are distributed along the x-axis for a sampling distribution of the sample mean?

A) scores
B) sample means
C) sample variances
D) sample means and sample variances

Question 15

What is the central limit theorem?

A) It explains that sample means will vary minimally from the population mean.
B) It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.
C) It explains that if we select a sample at random, then on average we can expect the sample mean to equal the population mean.
D) All of these.

Question 16

Suppose you select a sample of three people from a population of four (A,B,C,D).Which of the following samples is possible using the experimental sampling strategy?

A) persons A, C, and A
B) persons A, D, and D
C) persons B, C, and D
D) persons B, A, and B

Question 17

Experimental research is typically conducted using a sampling strategy in which

A) the order of selecting participants matters.
B) the same participant can never be selected twice in the same sample.
C) participants are replaced after being sampled.
D) all of these.

Question 18

The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1)

A) are both unbiased estimators.
B) both follow the central limit theorem.
C) are both associated with minimal variance.
D) all of these.

Question 19

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

A) The sample means will vary minimally from the population mean.
B) The sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.
C) If we select a sample at random, then on average we can expect the sample mean to equal the population mean.
D) All of these.

Question 20

A researcher selects a sample of size 6 from a population of size 10.How many possible samples of this size can be selected using theoretical sampling?

A) 100,000
B) 1,000,000
C) 10,000,000
D) over 60,000,000 samples

Question 21

A researcher selects two samples of 25 participants each.In the first sample,the population mean was 32 and the variance was 8.In the second sample,the population mean was 4 and the variance was 8.Which sample will be associated with a larger standard error of the mean?

A) Sample 1
B) Sample 2
C) None, both samples will have the same value for standard error.
D) There is not enough information to answer this question.

Question 22

The following samples were selected by two researchers.Which is associated with a smaller standard error of the mean?
Researcher A: n = 36, $\mu$ = 12, $\sigma$ = 9
Researcher B: n = 36, $\mu$ = 12, $\sigma$ = 6

A) Researcher A.
B) Researcher B.
C) They both have the same standard error.

Question 23

Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?

A) the central limit theorem
B) the skewed distribution rule
C) the fact that sample means vary minimally from the population mean
D) the fact that increasing sample size will decrease standard error

Question 24

A researcher selects two samples of 64 participants each.In the first sample,the population mean was 10 and the variance was 16.In the second sample,the population mean was 25 and the variance was 9.Which sample will be associated with a larger standard error of the mean?

A) Sample 1.
B) Sample 2.
C) None, both samples will have the same value for standard error.
D) There is not enough information to answer this question.

Question 25

The sample variance is an unbiased estimator of the population variance

A) when dividing SS by n.
B) when dividing SS by df.
C) when dividing SS by n - 1.
D) when dividing SS by df and when dividing SS by n - 1.

Question 26

Suppose that a researcher selects a sample of participants from a population.If the shape of the distribution in this population is positively skewed,then what is the shape of the sampling distribution of sample means?

A) approximately positively skewed
B) approximately negatively skewed
C) approximately normally distributed
D) there is not enough information to answer this question because the population mean and variance are not given

Question 27

Each of the following statements are true,except that

A) increasing the sample size will decrease standard error.
B) the larger the sample size, the larger the standard error.
C) the larger the standard deviation in the population, the larger the standard error.
D) the smaller the sample size, the larger the population size.

Question 28

A researcher increases the sample size,which will:

A) increase the value of standard error.
B) decrease the value of standard error.
C) reduce variability in the population.
D) increase variability in the population.

Question 29

Suppose that a researcher selects a sample of participants from a population.If the shape of the distribution in this population is negatively skewed,then what is the shape of the sampling distribution of sample variances?

A) approximately positively skewed
B) approximately negatively skewed
C) approximately normally distributed
D) there is not enough information to answer this question because the population mean and variance are not given

Question 30

Regardless of the shape of the distribution in the population,the sampling distribution of sample variances approximates a

A) normal distribution.
B) positively skewed distribution.
C) negatively skewed distribution.
D) multimodal distribution.

Question 31

In terms of estimating the population variance,what is one disadvantage of dividing SS by df to calculate sample variance?

A) It is an unbiased estimator.
B) It does not have minimum variance.
C) It underestimates the population variance on average.
D) None; there are no disadvantages of dividing SS by df to calculate sample variance.

Question 32

The mean of the sampling distribution of sample means is

A) equal to the population mean.
B) equal to the population variance.
C) equal to the population mean and equal to the population variance.
D) none of these.

Question 33

A researcher selects a sample of 16 participants from a population with a variance of 4.What is the standard error of the mean?

A) less than 1
B) equal to 1
C) greater than 1
D) there is not enough information to answer this question

Question 34

What characteristic of the sample variance do researchers generally consider more important: unbiased estimator or minimum variance?

A) minimum variance
B) unbiased estimator
C) Neither one; they are equally important.

Question 35

Two researchers select a sample from a population with a mean of 12.4 and a standard deviation of 9.Researcher A selects a sample of 30 participants.Researcher B selects a sample of 40 participants.Which sample is associated with a smaller standard error?

A) Researcher A's, because the sample size was smaller.
B) Researcher B's, because the sample size was smaller.
C) Researcher A's, because the sample size was larger.
D) Researcher B's, because the sample size was larger.

Question 36

The following samples were selected by two researchers.Which is associated with a smaller standard error of the mean?
Researcher A: n = 18, $\mu$ = 8, $\sigma$ = 2.4
Researcher B: n = 12, $\mu$ = 8, $\sigma$ = 2.4

A) Researcher A.
B) Researcher B.
C) They both have the same standard error.

Question 37

A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22.What is the standard error of the mean?

A) 32
B) 2.0
C) 0.5
D) There is not enough information to answer this question.

Question 38

As sample size increases,the standard error of the mean

A) increases.
B) decreases.
C) can increase or decrease.
D) does not change.

Question 39

The following samples were selected by two researchers.Which is associated with a smaller standard error of the mean?
Researcher A: n = 25, $\mu$ = 5, $\sigma$ = 7.
Researcher B: n = 25, $\mu$ = 32, $\sigma$ = 7.

A) Researcher A.
B) Researcher B.
C) They both have the same standard error.

Question 40

A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16.What is the standard error of the mean?

A) 10
B) 2.0
C) 0.5
D) There is not enough information to answer this question.

Question 41

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean of 13 or larger from this population?

A) equal to the probability of selecting a score above the mean
B) about one standard deviation below the mean
C) less than .10
D) greater than .31

Question 42

A sample mean is not always equal to a population mean.

Question 43

A sampling distribution is a distribution of all sample means or sample variances that can be obtained in samples of a given size from the same population.

Question 44

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20.About 68% of the sample means in this sampling distribution should be between a sample mean of

A) 18 and 58.
B) 34 and 38.
C) 38 and 44.
D) 36 and 40.

Question 45

For the experimental sampling strategy,the order in which a participant is selected does not matter,and once selected,each participant is not replaced before sampling again.

Question 46

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean that is at least equal to the population mean?

A) .50
B) equal to the probability of selecting a sample mean that is at most equal to the population mean
C) .50 and equal to the probability of selecting a sample mean that is at most equal to the population mean
D) none of these

Question 47

An article states that a sample of 40 participants took 12 ± 2.3 (M ± SEM)seconds to complete a cognitive assessment.Which value is the standard error of the mean?

A) 40
B) 12
C) 2.3
D) the standard error of the mean is not reported in the article

Question 48

Researchers typically sample with replacement,although the development of statistical theory was based on the use of sampling without replacement.

Question 49

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean equal to at least 12?

A) less than 1%
B) greater than 50%
C) about the same as selecting a sample mean that is at least equal to the population mean
D) equal to the probability of selecting a sample mean that is at most equal to 8

Question 50

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM)dollars on groceries each week.Which value is the standard error of the mean?

A) 112
B) 40
C) 100
D) the standard error of the mean is not reported in the article

Question 51

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?

A) .0228
B) .4772
C) .9772
D) equal to the probability of selecting a sample mean that is at least two standard deviations below the mean

Question 52

There are 25 possible samples of size 5 that can be selected from a population of 2 people using theoretical sampling.

Question 53

How is the standard error of the mean typically reported in a graph?

A) using error bars
B) by plotting sample means
C) by listing group names along the x-axis
D) it is never reported in a graph

Question 54

The sampling distribution of the mean is a distribution of all the possible samples of a particular size that can be selected from a given population.

Question 55

There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.

Question 56

A researcher selects a sample of nine participants from a population with a mean of 8 and a standard deviation of 3.About 14% of the sample means in this sampling distribution should be between a sample mean of

A) 6 and 8.
B) 5 and 6.
C) 9 and 10.
D) 10 and 11.

Question 57

The central limit theorem states that the sample mean will equal the population mean on average.

Question 58

The sampling distribution of the mean has minimum variance.

Question 59

Because the sampling distribution of sample means is normally distributed,we can use the z transformation formula to find probabilities.Which of the following gives the appropriate notation for this formula?

A)
B)
C)
D) all of these

Question 60

A sampling distribution is a distribution of scores in a population.

Question 61

The sampling distribution of sample variances is approximately normally distributed.

Question 62

The sample mean is an unbiased estimator of the population mean only when we divide SS by df.

Question 63

If data are reported as 12 ± 20 (M ± SEM),then the standard error of the mean is equal to 20.

Question 64

As sample size decreases,the standard error also decreases.

Question 65

The sample variance is an unbiased estimator of the population variance when dividing SS by df.

Question 66

As sample size increases,standard error decreases.

Question 67

The standard error is the sample mean divided by the square root of the sample size.

Question 68

The standard error of the mean is the standard deviation in a sampling distribution of sample means.

Question 69

The sample variance is an unbiased estimator of the population mean when dividing SS by df.

Question 70

The mean of a sampling distribution of sample means equals the population mean from which the samples were selected.

Question 71

Without knowing a thing about the population variance,we can expect a randomly selected sample variance (sample variance = SS/df)to equal the population variance on average.

Question 72

The sample mean is an unbiased estimator,follows the central limit theorem,and has minimum variance.

Question 73

A z transformation can be computed to locate sample means in a sampling distribution.

Question 74

The larger the population standard deviation,the smaller the standard error of the mean will be.

Question 75

The standard error of the mean is typically reported in a table or graph,but never in the text of a research article.

Question 76

If a researcher selects a sample with a mean of 8,then the mean of the sampling distribution of possible sample means will also equal 8.

Question 77

A researcher wants to select a sample of 30 participants from one of two populations.In Population A,the standard deviation is 12.In Population B,the standard deviation is 4.In this example,selecting a sample from Population A will produce the smallest standard error.

Question 78

A researcher selects a sample of 169 participants from a population with a mean of 50 and a standard deviation of 13.The probability of selecting a sample mean that is less than 49 is .8413.

Question 79

If a researcher selects a sample of 64 participants from a population with a variance of 16,then the standard error of the mean will be 2.0.

Question 80

We can find the probability of obtaining a sample mean from a population using the standard normal distribution.