Test Bank

Chapter 7: Population, Sample, and Sampling Distributions

Multiple Choice

1. An empirical distribution consisting of raw scores taken from a population is referred to as what by research scientists?

A. a sample distribution

B. the standard normal curve

C. a population distribution

D. the t distribution

2. An empirical distribution consisting of raw scores taken from a sample is referred to as ______ in scientific research?

A. a sample distribution

B. a population distribution

C. the standard normal curve

D. the t distribution

3. A theoretical distribution made up of infinite sample statistics is referred to as ______.

A. a population sample

B. a sample population

C. a population distribution

D. a sampling distribution

4. Sample statistics vary from sample to sample. Why is this potentially problematic?

A. Before inferential statistics can be calculated, a static empirical environment must be created.

B. Sampling error is introduced.

C. Excess variation ultimately leads to increased standard error and skewing of results.

D. Excess variance will lead to increased standard error of the mean, resulting in skewed results.

5. The central limit theorem states ______.

A. That whenever descriptive statistics are to be computed, the sample statistic must exceed the sampling distribution mean.

B. Prior to the calculation of inferential statistics, basic descriptive results must be generated to act as a bridge between the theoretical distributions and the empirical observations.

C. Prior to the calculation of descriptive statistics, an infinite number of large samples must be drawn from the population under study, thus ensuring a normally distributed sample.

D. That any time descriptive statistics are computed from an infinite number of large samples, the resulting sampling distribution will be normally distributed.

6. The mean of the sampling distribution is equal to ______.

A. the true population mean

B. the true sample mean

C. the standard error of the median

D. the sample mode

7. The standard deviation of the sampling distribution is also called ______.

A. the standard error of the median

B. the standard median

C. the standard error

D. the standard mean

8. A professor studying crime and environmental design draws a random sample of neighborhoods from a city. If this is his sample, what is the population to which he will be able to generalize the results of his statistical analyses?

A. all neighborhoods in the city from which the sample was drawn

B. all individual people in the city

C. neighborhoods in the state in which the city is located

D. neighborhoods nationwide

9. A professor studying crime and environmental design has a sample of 25 neighborhoods. Which probability distribution should he use?

A. the z distribution

B. the t distribution

C. either z or t

D. none of these; no statistics can be computed on such a small sample

10. What is the minimum sample size necessary for the z distribution to be used?

A. 40

B. 70

C. 100

D. none of these; sample size for the z distribution does not matter as the curve is appropriate for any sample size.

11. What is the area under the t distribution curve?

A. 1.00

B. 0.50

C. 100

D. 3.14

12. Which of the following is an important distinction between the z and t distributions?

A. The t distribution changes shape depending on sample size; the z distribution does not.

B. The t distribution does not differ from the z distribution; it is simply another theoretical construct available for use by research scientists.

C. The z distribution changes shape depending on sample size; the t distribution does not.

D. The z distribution is normally distributed, whereas the t distribution is skewed.

13. Under which of the following conditions does the t distribution begin to resemble the normal curve?

A. as the sample size increases

B. as the sample size decreases

C. when the sample size is exactly 88

D. none of these; there are no conditions under which the t distribution resembles the z distribution

14. Which of the following is true about the t distribution?

A. It is bimodal.

B. It is unimodal.

C. It does not change its shape under any circumstances or conditions.

D. The area under the curve equals 0.50.

15. Generally speaking, large samples are those containing at least how many cases?

A. 50

B. 100

C. 25

D. 500

16. The Greek symbol “μ” is used to represent which of the following?

A. the mean for a population

B. the mean for a sample

C. the standard error

D. the sampling error

17. The Greek symbol “σ” is used to represent which of the following?

A. the standard error for a sample

B. the sampling error of the mean

C. the standard deviation for a population

D. the mean for a sample

18. What is meant by the term parameter?

A. A parameter is a number based on sample data.

B. A parameter is simply another term for a statistic.

C. A parameter is a number based on an empirical observation.

D. A parameter is a number based on population data.

19. What is one characteristic of a parameter that makes it differ from a statistic?

A. It is a static, unchanging constant used in the calculation of the standard error, while a statistic is used only in basic descriptions of a sample.

B. A parameter is fixed, while it is possible for a statistic to vary from sample to sample.

C. A parameter is able to vary from case to case, while a statistic is constant and unchanging.

D. A parameter is used with sample data, while a statistic is used only with populations.

20. A parameter can have exactly how many means?

A. 2

B. 0

C. 1

D. There is no limit to the number of means for a parameter.

21. Which of the following is the reason that sampling distributions are theoretical constructs as opposed to empirical distributions?

A. Sampling distributions are based on the notion of drawing infinite samples from a single population, something that is impossible in reality.

B. Sampling distributions are made of raw scores.

C. Sampling distributions are made from the t curve.

D. None of these; sampling distributions are not theoretical constructs; empirical distributions are theoretical in nature.

22. Name a second characteristic of sampling distributions that make them different from empirical sample distributions.

A. Sampling distributions are created from raw scores whereas empirical distributions are generated from sample statistics.

B. Sampling distributions are tangible entities, whereas empirical distributions are purely theoretical constructs.

C. Sampling distributions are created not from raw scores but from sample statistics.

D. Sampling distributions are used only in the calculation of sampling error, while empirical observations are used in the theoretical construction of the z and t distributions.

23. The sampling distribution clusters around the actual population ______.

A. mean

B. parameter

C. statistic

D. mode

24. In instances where N ≤ 99, researchers work with the ______ rather than the z distribution.

A. population distribution

B. standard deviation

C. population mean

D. t distribution

25. When samples are ______, though the sampling distribution cannot be assumed to be normal.

A. large

B. unknown

C. small

D. weak

26. A ______ distribution contains all values in a population.

A. normal

B. sample

C. skewed

D. population

27. Statistics are estimates of population ______.

A. parameters

B. vectors

C. distributions

D. none of these

28. Statistics vary from sample to sample because of ______.

A. user error

B. normal error

C. sampling error

D. population error

29. The standard deviation of a sampling distribution is the ______.

A. population parameter

B. variance

C. range

D. standard error

30. One of the most important theoretical ideas in statistics is the ______, which states that the sampling distribution will be normally distributed when infinite samples of a large size are drawn.

A. central limit theorem

B. bounding rule

C. rule of the complement

D. none of these

31. Which of the following is a type of distribution?

A. population

B. sample

C. sampling

D. all of these

32. ______ samples are more accurate representations of the population sample.

A. Small

B. Rhetorical

C. Large

D. None of these

33. ______ distributions are theoretical.

A. Population

B. Sampling

C. Sample

D. none of these

34. ______ distributions are created from sample statistics.

A. Population

B. Sampling

C. Sample

D. none of these

35. Generally is not advisable to work with samples smaller than ______.

A. 100

B. 100–500

C. 500–1,000

D. none of these

1. A population is the entire universe of objects, people, places, or other units of analysis that a research scientists wishes to study.

2. Statistics are estimates of population parameters that contain sampling error.

3. Population parameters vary from sample to sample because of sampling error.

4. A population distribution contains a select subset of the values occurring within an entire population.

5. The central limit theorem states that statistics derived from infinite samples of large size will produce a sampling distribution that is normal in shape.

6. In the t distribution, when a sample size is small, the curve is tall and narrow.

7. In the t distribution, as sample size increases, the curve becomes more and more normal until it looks identical to the z curve.

8. The area under the curve of the t distribution changes as sample size fluctuates.

9. The area under the curve of the t distribution is equal to 1.00.

10. The t distribution is a unimodal distribution.

11. The t distribution changes shape depending on sample size.

12. The t distribution resembles the z distribution in that it is symmetrical.

13. In those cases where a research scientist has a sample of size N ≤ 99, it is wise for an analysis to make use of the z distribution.

14. In order for a research scientist to be able to work with the z distribution, the sample size must be at least as large as N ≥100.

15. Generally speaking, a sample needs to contain at least N ≥ 100 cases in order for the central limit theorem to be true.

16. A sample distribution shows the shape and form of the values in a sample taken from a population.

17. A sampling distribution is a theoretical distribution made up of infinite sample statistics.

18. Population and sample distributions are both empirical because they exist in reality.

19. A parameter is a number derived from sample data.

20. A statistic is a number derived from population data.

1. Define the central limit theorem.

2. Explain why researchers do not usually examine populations directly.

3. Why is the central limit theorem important to criminal justice research?

4. If the central limit theorem is so important, what is the key benefit of having a sampling distribution that is normally distributed in research?

5. Explain what is meant by sampling error.