Sampling Test Bank Answers Chapter 6

CHAPTER 6

Sampling

Multiple Choice

1. According to the textbook authors, in social research,
   1. a census of the population is always more accurate than a sample of the population.
   2. the more homogeneous the population, the greater the need to rely on a sample of cases rather than a single case.
   3. practical considerations such as time and cost usually necessitate sampling.
   4. no sample can adequately represent human variability.
2. A primary reason for the Literary Digest poll’s erroneous forecast that Landon would win the 1936 presidential election was
   1. the large proportion of undecided voters at the time of the poll.
   2. the small sample upon which the poll was based.
   3. an inadequate sampling frame that systematically excluded the poor.
   4. the use of mailed questionnaires rather than more reliable face-to-face interviews.
3. In the National Health and Social Life Survey, “all people aged 18 to 59 with adequate English proficiency living in households located in the 50 states and District of Columbia” describes the
   1. target population.
   2. sampling frame
   3. sample.
   4. sampling distribution.
4. Defining the population in a survey is a two-step process. The first step consists of defining the __________; the second step consists of constructing the __________.
   1. unit of analysis; target population
   2. target population; sampling frame
   3. sampling frame; sample design
   4. sampling design; sample
5. To measure women’s leadership in local government, a researcher obtains a list of all cities in the U.S., randomly selects 100 cities, and identifies whether the mayor of each selected city is a man or woman in the year 2017. What is the researcher’s sampling frame?
   1. list of all U.S. cities
   2. list of all mayors in 2017
   3. list of all women mayors in 2017
   4. the 100 selected cities
6. For a survey of senior citizens, a copy of the annual city census is obtained, and 30,000 residents sixty-five years of age and older are identified. A total of 400 seniors is selected, of whom 250 are interviewed. There are __________ senior citizens in the sampling frame.
   1. 30,000
   2. 400
   3. 250
   4. an unknown number of
7. Suppose you use the campus directory to draw a sample of the student population. When you draw your sample you discover that ten students have no telephone number listed; and when you conduct the survey, you discover that five students have an incorrect number listed. These “missing cases” indicate problems with
   1. the specification of the target population.
   2. the sampling design.
   3. the sampling frame.
   4. random sampling error.
8. It is best to use probability sampling when
   1. trying to understand the context of people’s actions.
   2. studying a small number of cases.
   3. the population is unknown or not readily identifiable.
   4. the research objective is to estimate population characteristics.
9. What is the key feature of probability sampling that distinguishes it from nonprobability sampling?
   1. selection of very large samples.
   2. elimination of sampling error.
   3. use of random selection.
   4. reduction of bias in the sampling frame.
10. What defining feature of a simple random sample distinguishes it from other probability sampling designs?
    1. It does not require a sampling frame for the selection of cases.
    2. Every case is randomly selected.
    3. Every case has a known probability of being selected.
    4. Every combination of cases has an equal chance of being selected.
11. Parameter is to __________ as statistic is to __________.
    1. measurement; sampling
    2. population; sample
    3. mean; standard error
    4. standard error; mean
12. Consider the variable cumulative grade-point average (GPA). Suppose you select a simple random sample of 100 students from the population of all currently enrolled students at your college. A sampling distribution would consist of the distribution of
13. GPAs for all currently enrolled students.
14. average GPAs for all possible samples of 100 students.
15. GPAs for the simple random sample of 100 students.
16. average GPAs for two or more subsamples, such as male and female students.
17. Which of the following describes a sampling distribution?
    1. distribution of individual responses in a single sample
    2. distribution of individual responses in a population
    3. probability distribution of individual responses in a single sample
    4. probability distribution of a sample statistic
18. A researcher draws a random sample of 100 full-time city employees and, based on their self-reported salaries, calculates an average annual salary of $56,000. According to city records, however, the average annual earnings of all full-time city employees is $51,000. Which of the following conclusions can you draw from these data?
    1. The mean of the sampling distribution for samples of 100 is $51,000.
    2. The estimated margin of error for all samples of 100 is $5,000.
    3. The sample estimate is based on a biased sample of city employees.
    4. The sample is too small to provide an accurate estimate of the average earnings of all employees.
19. Knowledge of the sampling distribution of a statistic enables researchers to
    1. draw a smaller sample than ordinarily would be necessary.
    2. estimate the probable margin of error of a sample statistic.
    3. calculate the population value.
    4. calculate the difference between a population value and a sample estimate.
20. To calculate the margin of error of a sample estimate, you must know all but which one of the following?
    1. size of the sample
    2. standard error of the sampling distribution
    3. the population value
    4. desired level of confidence in the margin of error
21. Knowledge of the sampling distribution of a statistic enables researchers to
    1. draw a smaller sample than ordinarily would be necessary.
    2. estimate the range of probable error of a sample statistic.
    3. calculate the population parameter.
    4. calculate the difference between a parameter and a statistic.
22. The two main reasons for using stratified sampling are to __________ and to __________.
    1. decrease the margin of error; increase the number of cases in particular subgroups
    2. decrease sampling costs; decrease the margin of error
    3. analyze the effects of the stratified variable; increase the number of cases in particular subgroups
    4. decrease sampling costs; analyze the effects of the stratified variable
23. A stratified random sample reduces error when
    1. an equal number of cases is drawn from each stratum.
    2. the stratifying variable is related to the variable under study.
    3. the differences between strata are relatively small.
    4. the number of cases in each stratum of the sample is proportionate to the number of cases in the population.
24. In a disproportionate stratified sample,
    1. a different proportion of cases is drawn from each stratum.
    2. the proportion of cases in each stratum of the sample differs from the proportion of cases in each stratum of the population.
    3. a different number of cases is drawn from each stratum.
25. A multistage cluster sample would be most appropriate for an interview study of which of the following populations?
    1. all rape victims in your state during the year 2015
    2. all students currently enrolled at your college
    3. followers of the Grateful Dead rock group
    4. all first-year law students in the United States
    5. all students at your college who use nonprescription drugs
26. Multistage cluster sampling
    1. is a means of drawing a probability sample when a list of the target population is unavailable.
    2. is superior to stratified random sampling, given equivalent costs.
    3. would be appropriate for a geographically concentrated population, such as students at a particular college.
    4. is rarely used in face-to-face interview surveys because it is difficult to implement.
27. Which type of sampling design uses probability proportionate to size sampling?
    1. simple random sampling
    2. systematic sampling
    3. stratified random sampling
    4. multistage cluster sampling
    5. purposive sampling
28. Stratified random sampling is used to __________ ; multistage cluster sampling is used to __________.
    1. reduce costs; eliminate the need to list sample elements
    2. reduce sampling error; reduce sample size
    3. reduce sample size; reduce sampling error
    4. reduce sampling error; reduce costs
29. A stratified random sample reduces sampling error to the extent that variation within each stratum is __________; the sampling error of a cluster sample is reduced to the extent that variation within clusters is __________compared with the variation across clusters.
    1. small; small
    2. small; large
    3. large; small
    4. large; large

1. When properly executed, which of the following probability sampling designs requires the fewest cases for a given level of sample accuracy?
   1. simple random
   2. stratified random
   3. multistage cluster
2. Because of the ready availability of electronic lists and computer programs for random selection, this sampling method is seldom used today.
   1. simple random sampling
   2. systematic sampling
   3. proportionate stratified random sampling
   4. single-stage cluster sampling
   5. three-stage cluster sampling
3. To obtain a systematic random sample of size 100 from a population of size 3,000, one must first select a random case between 1 and ________ and then select every ________th case thereafter.
   1. 100; 100
   2. 100; 30
   3. 10; 30
   4. 30; 30
4. If the researcher is unable to obtain a list of the population or members of the population cannot be identified easily, then he or she must use a
   1. very large sample.
   2. representative sample.
   3. probability sample.
   4. nonprobability sample.
5. Under which of the following conditions would nonprobability sampling be most appropriate?
   1. very few cases can be included in the sample
   2. a list of the target population is readily available
   3. accurate estimates of certain population characteristics are required
   4. there is a clear basis for judging what cases would be representative of the population
6. You need a sample of twenty-five students to interview for a study of attitudes toward intercollegiate athletics, and so you interview the first twenty-five students to enter the campus center on a Monday morning. What kind of sample is this?
   1. convenience sample
   2. purposive sample
   3. snowball sample
   4. simple random sample
7. Which of the following sampling techniques depends for its effectiveness largely on the researcher’s knowledge and skill in selecting appropriate cases?
   1. convenience sampling
   2. simple random sampling
   3. purposive sampling
   4. multistage cluster sampling
8. Which of the following sampling designs controls for the biased selection of respondents?
   1. convenience sampling
   2. purposive sampling
   3. snowball sampling
   4. simple random sampling
9. Stratified sampling and quota sampling are similar in that both
   1. are probability techniques.
   2. require some knowledge of population characteristics prior to sample selection.
   3. increase the sampling error.
   4. require larger samples than other sampling techniques.
10. Which of the following nonprobability sampling designs most closely resembles stratified random sampling?
    1. convenience sampling
    2. purposive sampling
    3. quota sampling
    4. snowball sampling
11. Suppose you are working with the vice squad in your city to conduct an interview study of female prostitutes. Which of the following sampling designs would be best to select your interviewees?
    1. simple random sampling
    2. stratified random sampling
    3. multistage cluster sampling
    4. snowball sampling
12. Network sampling and snowball sampling are recommended when
    1. sampling a target population that comprises a very small subgroup of a larger population.
    2. probability sampling is necessary.
    3. studying past events.
    4. studying very small populations with fewer than two hundred cases.
13. For which of the following populations would some form of referral sampling (network sampling or snowball sampling) be appropriate?
    1. all students currently enrolled at your college
    2. all students currently enrolled in U.S. colleges and universities
    3. all students at your college who use nonprescription drugs
    4. all sociology majors at your college
    5. all female sociology majors at your college
14. You plan to draw a sample of 1,000 from the population of a large state in order to estimate the average value of individual life insurance coverage. A list of all state residents and their incomes is available from the state revenue department. Which sampling design will minimize sampling error?
    1. a simple random sample, using a computer program to generate random numbers
    2. a proportionate stratified random sample, using income categories as strata
    3. a multistage cluster sample, using counties as clusters
    4. a quota sample, with quotas set on the basis of income
15. Suppose you want to estimate the average number of courses that students at your school take in the natural sciences. The registrar provides a complete list of student names, along with each student’s campus or local address, class year, and major. Assuming that you can only select 100 students, your best estimate would probably come from a
    1. simple random sample.
    2. systematic sample.
    3. stratified random sample, stratifying on student major.
    4. cluster sample, with student residence halls serving as the clusters.
    5. quota sample, with twenty-five students selected from each class.
16. Which of the following considerations is least important in determining sample size?
    1. heterogeneity of the population
    2. degree of error tolerated in the sample estimate
    3. cost per case
    4. size of the population
17. What are the two most important considerations in determining an appropriate sample size?
    1. size of the population; complexity of the sampling design
    2. available resources; size of the population
    3. available resources; desired precision
    4. desired precision; size of the population
18. Which of the following principles applies to probability sampling?
    1. The larger the population, the larger the standard error.
    2. The larger the population, the larger the sample necessary for a given margin of error.
    3. The larger the sample, the smaller the standard error.
19. Suppose a student doing a telephone survey for the campus newspaper asks you, “How big a sample do I need to get accurate results?” Which of the following would be the best advice you could offer?
20. The number of cases should be at least 25 percent of the population.
21. Only samples of 3,000 or more yield truly accurate results.
22. That depends on the number of students at the college. The proportion of the population sampled is more important than the absolute size of the sample.
23. Accuracy (in terms of error reduction) improves much more for increases in sample size between 100 and 1,000 than for increases in sample size between 2,000 and 3,000.
24. For a numerical variable, say income, which of the following statistics has the smallest value?
    1. standard deviation of a sample for a sample size of 100
    2. standard deviation of a sample for a sample size of 500
    3. standard error of the sampling distribution for samples of size 100
    4. standard error of the sampling distribution for samples of size 300
25. In probability sampling, which of the following results in random sampling error?
    1. an incomplete sampling frame
    2. refusals to cooperate
    3. random selection
    4. failures to contact sampled respondents
26. Which of the following statements is false regarding sampling error?
    1. Sampling error exists whenever researchers rely on a sample to estimate population parameters.
    2. Sampling error depends on the type of sampling design.
    3. One of the most important determinants of sampling error in probability sampling is sample size.
    4. It is much easier to detect and estimate nonrandom sampling error than random sampling error.
27. __________ produces random sampling error, whereas __________ is a source of sample bias.
    1. An incomplete sampling frame; refusals to cooperate
    2. Random selection; failures to contact sampled respondents
    3. Refusals to cooperate; an incomplete sampling frame
    4. Failures to contact sampled respondents; random selection
28. Which of the following is a source of coverage error?
    1. an incomplete sampling frame
    2. refusals to cooperate
    3. unreturned questionnaires
    4. item nonresponse
    5. random selection processes
29. When pollsters conduct telephone polls, they typically use random-digit dialing; however, some people refuse to cooperate and answer the questions, and others are not at home when called. This results (or may result) in
    1. coverage error due to an incomplete sampling frame.
    2. an increase in random sampling error.
    3. nonresponse error or sample bias.
    4. measurement error.
30. Which of the following questions would be least relevant in judging the overall quality of a sample?
    1. Is it a probability or nonprobability sample?
    2. How complete was the sampling frame?
    3. What was the response rate?
    4. Was the sampling design single or multistage?

True and False

T F 1. The sampling frame is a type of probability sample.

T F 2. If you used the campus directory to sample students on your campus, all students listed in the directory would be the sampling frame.

T F 3. Ideally, the sampling frame should be identical to the target population.

T F 4. For a city telephone survey, a sampling frame might consist of the set of all telephone prefixes (first three numbers after the area code) for the city.

T F 5. Drawing a simple random sample requires the random selection of cases from a list of the population.

T F 6. Representativeness is the best measure of the overall quality of a sample.

T F 7. Probability sampling is to nonprobability sampling as random selection is to nonrandom selection.

T F 8. A sampling distribution describes how a sample statistic is likely to vary about the population value it estimates.

T F 9. The larger the sample, the larger the standard error.

T F 10. Sampling error can be eliminated by drawing a probability sample.

T F 11. Probability sampling enables researchers to calculate the margin of sampling error.

T F 12. Given the same standard error, a 99 percent confidence interval is smaller than a 95 percent interval.

T F 13. To use stratified random sampling, the sampling frame must contain information on the stratifying variable.

T F 14. A stratified random sample decreases sampling error to the extent that the differences between strata are large compared with differences within strata.

T F 15. In stratified random sampling, different numbers of cases may be drawn from each stratum.

T F 16. Proportionate stratified sampling requires that the same number of cases be drawn from each stratum.

T F 17. The general purpose of multistage cluster sampling is to reduce the costs of data collection.

T F 18. Multistage cluster sampling is most appropriate for small, geographically concentrated populations.

T F 19. Multistage cluster sampling may involve either simple random or stratified random sampling at each stage.

T F 20. Given equivalent costs, multistage cluster sampling is superior to simple random sampling.

T F 21. Systematic sampling is the most basic sampling design and is found in the more complex designs such as stratified sampling.

T F 22. Probability sampling is always preferable to nonprobability sampling.

T F 23. Nonprobability sampling generally is more appropriate in the early than in the late stages of research.

T F 24. Purposive sampling should be used when very little is known about the population.

T F 25. Snowball sampling is often used in studies of deviant behavior.

T F 26. The cases or observations selected in nonprobability sampling may provide a basis for statistical inference.

T F 27. One of the most important determinants of sample size is cost.

T F 28. In general, the greater the heterogeneity of the population, the larger the sample required for a given level of precision.

T F 29. In determining the accuracy of sample estimates, the proportion of the population sampled is more important than the absolute size of the sample.

T F 30. Increasing sample size from 100 to 500 increases sample precision more than increasing sample size from 1,000 to 5,000.

T F 31. Random selection produces random sampling error.

T F 32. Incomplete sampling frames generally result in random as opposed to systematic sampling error.

T F 33. Probability sampling designs eliminate coverage error and nonresponse bias.

Essay

1. Describe the key differences between probability and nonprobability sampling. What defines a probability sample? For what purposes and under what conditions is it appropriate to use each of these sampling strategies? What kind of inferences are possible with each?
2. Suppose you want to draw a probability sample of all U.S. intercollegiate athletes who are competing during the current academic year. Describe how you might use each of the basic probability sampling designs: simple random, stratified random, and multistage cluster. Then indicate which sampling design you think is best to use and why.
3. To study how satisfied Americans are with the electoral process, a social scientist conducts a mail questionnaire survey. First he obtains a list of all political precincts in the United States (which covers all areas of the United States) and randomly selects a number of precincts from this list. He then obtains a list of registered voters for each selected precinct, and from each list he selects a random sample of voters. Finally, he mails each selected voter a survey in which he asks questions about their satisfaction with the electoral process.
   1. What type of sampling design is this?
   2. There are two sampling frames. What are they?
   3. Carefully evaluate the adequacy of each frame in terms of meeting the objective of the study—to assess Americans’ satisfaction with the electoral process?
4. Suppose you want to study registered nurses; you are particularly interested in comparing the careers and earning of men and women in this profession. You realize that female nurses outnumber male nurses by a ratio of about 9 to 1. You also discover a national registry of nurses contains a publicly accessible list of all nurses in the U.S. Suppose you have enough funds to draw a sample of 500 for a mail questionnaire survey.
   1. What would be a good sampling frame for this study?
   2. Would you choose to use multistage cluster sampling? Briefly explain.
   3. Why would it be advisable to draw a stratified random sample rather than a simple random sample for your study?
   4. Suppose you decide to draw a stratified random sample. What information must you have about each respondent in order to draw a stratified random sample?
   5. Would it be best to use proportionate stratified random sampling or disproportionate stratified random sampling? Briefly explain.
5. Following a senatorial election in California, a Los Angeles Times article pointed out that the polls are not as reliable as media portrayals would suggest. The author gave several examples of seemingly contradictory poll results in pre-election surveys; for example, one poll had one candidate ahead by 10 points and another poll had her trailing by 2. Suppose someone asks you to explain how this could occur. Assuming that all the polls were telephone surveys that used probability sampling, identify and briefly describe three possible sources of sampling error in the polls.