Sampling Techniques and Sampling Distribution - Quiz Questions and Answers

1. 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

2. 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 the above

3. 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.

4. 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.

5. A researcher selects two samples of 25 participants each. In the first sample the population mean was 32 and the variance was 8. In this 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

6. 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.

7. The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?

Researcher A: n = 36, = 12, = 9

Researcher B: n = 36, = 12, = 6

A) Researcher A

B) Researcher B

C) They both have the same standard error.

8. The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?

Researcher A: n = 18, = 8, = 2.4

Researcher B: n = 12, = 8, = 2.4

A) Researcher A

B) Researcher B

C) They both have the same standard error

9. 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 .03

D) Greater than .31

10. 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) 0.0228

B) 0.4772

C) 0.9772

D) Equal to the probability of selecting a sample mean that is at least two standard deviations below the mean.

11. A researcher selects a sample of 9 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

12. 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.