Chapter 14: Sample Size Determination
Multiple Choice
1. Which of the following is not a piece of required information in order to
determine sample size?
a. estimated population standard deviation
b. estimated population median
c. acceptable level of sampling error
d. desired level of confidence
e. All are necessary to determine sample size.
2. The idea that a large number of sample means or proportions will approximate a
normal distribution, regardless of the distribution of the population from which
they were drawn, is known as:
a. sample variance.
b. population variance.
c. central limit theorem.
d. random error.
e. none of the above
3. A continuous distribution, which is bell-shaped and symmetric about the mean, is
known as:
a. the normal distribution.
b. the chi-square distribution.
c. the F-distribution.
d. the mean distribution.
e. the binomial distribution.
175
Difficulty: Easy
Response: See page 409
Ref: Normal Distribution
Learning Objective 14.3: To gain an appreciation of a normal distribution.
4. A researcher wants to know the average number of times per month respondents
eat at fast food restaurants. The statistic that s/he is most interested in would be
the_________.
a. variance
b. mean
c. standard deviation
d. proportion
5. Researchers can determine via statistical techniques sample size. However, these
techniques can only be applied to which of the following types of sample?
a. cluster
b. simple random
c. nonprobability
d. stratified
e. none of the above
6. Which of the following is not a determinant of sample size for probability
samples?
a. budget available
b. research objectives
c. rule of thumb
d. none of the above
176
Difficulty: Easy
Response: See page 407-408?
Ref: Determining Sample Size for Probability Samples
Learning Objective 14.2: To discover methods for determining sample size.
7. If we were making inferences from a single sample, we would expect that there
would be a ____ percent probability that the sample mean or proportion generated
from our sample results would be within two standard errors of the true
population mean.
a. 68.26%
b. 99.74%
c. 97.5%
d. 95.44%
e. 98.00%
8. Higher levels of confidence generally require:
a. larger sample sizes.
b. greater variance.
c. smaller sample sizes.
d. smaller standard deviation.
9. When a research company routinely uses samples of 300 for their studies, they are
using which type of plan to determine sample size?
a. the 50% rule
b. budget available
c. rule of thumb
d. number of subgroups to be analyzed
177
Response: See page 407
Ref: Determining Sample Size for Probability Samples
Learning Objective 14.2: To discover methods for determining sample size.
10. How many respondents should be in each important subgroup of a sample?
a. 10
b. 25
c. 50
d. 100
11. Which of the following statements about sample size is false?
a. There is no direct relationship between population size and the size of the
sample required to estimate population parameters.
b. The larger the sample variance, the larger the sample size that is required.
c. The higher the level of confidence, the larger the sample size that is
required.
d. The larger the population, the larger the sample size that is required.
e. All of the above statements are false.
12. Holding constant at a 95% level of confidence, if the standard deviation increases,
then the sample size required to represent the population in question will be
_______.
a. larger
b. about the same
c. smaller
d. not applicable
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Ref: Determining Sample Size
Learning Objective 14.4: To understand population, sample, and sampling
distributions.
13. As the level of tolerable error increases in the sample means formula, the sample
size required to represent a particular population is:
a. smaller.
b. larger.
c. about the same.
d. none of the above
14. Which of the following are not required to determine sample size using the
sample means formula?
a. the standard error of the mean
b. desired level of confidence
c. estimate of population standard deviation
d. level of tolerable error
e. All of the above are required.
15. Which of the following is not a method for estimating the population standard
deviation?
a. prior study results
b. conduct a pilot study
c. use secondary data
d. using population size
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Learning Objective 14.4: To understand population, sample, and sampling
distributions.
16. ____________ is a range of values within which the true population value is
estimated to fall.
a. Interval estimate
b. Point estimate
c. Population estimate
d. Sample estimate
e. none of the above
17. Which of the following is not a measure of central tendency?
a. variance
b. mean
c. median
d. mode
18. Standard error of the mean is:
a. a measure of dispersion of a large population.
b. a measure of dispersion of large sample.
c. the standard deviation of a distribution of sample means.
d. the error in the computation of population standard deviation.
e. none of the above
19. All of the statistical methods for determining sample size in this chapter assume
which of the following?
a. a large population
b. a valid questionnaire
c. simple random sampling
d. stratified sampling
e. none of the above
20. Which of the following would increase the necessary sample size in a study?
a. smaller mean of the variables in question
b. less need for precision
c. need to divide sample into sub-groups
d. larger population
e. none of the above
21. About 68% of the area under a standard normal curve covers one _________.
a. mean
b. sample
c. variance
d. standard deviation
e. none of the above
22. When a researcher is not sure if people who responded to the survey are different
from those who did not respond, this brings into question the issue of:
a. inappropriate sample size.
b. systematic bias.
c. nonresponse bias.
d. refusal bias.
23. A ____________ normal distribution is a normal distribution with a mean of zero
and a standard deviation of one.
a. Balanced
b. Standard
c. Stock
d. Ordinary
24. The _____________ includes all the possible individuals or objects from whom
or about which information is needed to meet the objectives of the research.
a. Group
b. Selection
c. Population
d. Range
25. ___________ sampling error is the amount of sampling error the researcher is
willing to accept.
a. Given
b. Projected
c. Accepted
d. Allowable
26. The greater the number of subgroups to be analyzed, the smaller the necessary
sample size.
27. In a normal distribution, the mean, median, and mode are equal.
28. If large enough samples are taken, most human behavior can be plotted using a
normal distribution curve.
29. Theoretically, the sampling distribution of the mean is always normally
distributed.
30. Population size is the most important determinant of effective sample size.
31. A normal distribution has a total of 6 standard deviations.
32. The level of tolerable error (e) in the sample proportions formula is expressed in
terms of a percent.
33. Some normal distributions cannot be transformed into standard normal
distributions.
34. A range of values with which the true population value is estimated to fall is
known as the point estimate.
35. A confidence interval always includes the true population value.
36. Budget is rarely a consideration when determining sample size.
37. Subgroups are often chosen based on demographics of the sample, such as gender,
income, etc.
38. If a researcher takes enough samples, the data will begin to approach a normal
distribution.
39. The “budget available” approach forces the researcher to explore alternative data–
collection approaches and to carefully consider the value of information in
relation to cost.
40. The total area under a normal curve is not equal to one, meaning all observations.
41. The finite population correction factor (FPC) is an adjustment to the required
sample size that is made in cases where the sample is expected to be equal to 5
percent or more of the total population.
42. Statistical power is the probability of making a type II error.
Essay Questions
43. Assuming the research objectives of the study can be accomplished, researchers
would much prefer to estimate the required sample size using the sample
proportion formula rather than the sample means formula. Why?
44. Compute the required sample size given the required confidence in the sample
results is 90%. The level of tolerable sampling error is 1% and the estimated
population standard deviation is 5.
45. A researcher is conferring with a client to do a telephone interview for a particular
topic, which the researcher will subcontract to a field services firm for $10 per
usable response. The researcher’s client wants to be 95.44% confident of the
results. Assume the sample proportions formula is appropriate, and that the level
of tolerable sample error is 4%. The budget for data collection only offered by
the client can be up to but not over $10,000. How many usable responses are
needed for the given level of confidence and much will the subcontractor charge
the market researcher for sampling? Is the budget for data collection large
enough?
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3) Cost of sampling: $10 x 625 = $6,250
4) Data Collection budget is $10,000
5) The budget is large enough
Difficulty: Hard
Ref: Determining Sample Size
Learning Objective 14.1: To learn the financial and statistical issues in the
determination of sample size.
46. A researcher wants to estimate the percentage of all adults that have used the
Internet to seek pre-purchase information in the past 30 days, with a tolerable
sampling error (E) of 0.03 and a confidence level of 97.5%. If secondary data
indicated that 25% of all adults had used the Internet for such a purpose, what is
the sample size?
47. A researcher wants to estimate a population mean. The level of tolerable
sampling error is 0.2 of a purchase occasion, with a confidence level of 95.44%.
If the estimated population variance is 5 for the most important question in the
study, what is the desired sample size?