Name:
Class:
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Indicate whether the statement is true or false.
1. The size of a sample can be selected by first determining the desired standard error and then using the formula
to calculate n.
a.
True
b.
False
2. In cluster sampling, the population is divided into subsets called clusters (such as cities or city blocks), and then a
random sample of the clusters is selected. Once the clusters are selected, we typically sample all of the members in each
selected cluster.
a.
True
b.
False
3. Simple random sampling can result in under-representation or over-representation of certain segments of the
population. This is one of several reasons that simple random samples are almost never used in real applications.
a.
True
b.
False
4. We can measure the accuracy of judgmental samples by applying some simple rules of probability. This way,
judgmental samples are not likely to contain our built-in biases.
a.
True
b.
False
5. A probability sample is a sample in which the sampling units are chosen from the population by means of a random
mechanism such as a random number table.
a.
True
b.
False
6. Stratified samples are typically not used in real applications because they provide less accurate estimates of population
parameters for a given sampling cost.
a.
True
b.
False
7. Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.
a.
True
b.
False
8. A simple random sample is one where each member of the population has a known chance (this may differ from one
member to another) or probability of being chosen.
a.
True
b.
False
9. If the sample size is greater than 30, the Central Limit Theorem (CLT) will always apply.
a.
True
b.
False
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10. The standard error of sample mean is large when the observations in the population are spread out (large ),
but that the standard error can be reduced by taking a smaller sample.
a.
True
b.
False
11. One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum – which we
would not obtain if we took a simple random sample from the entire population. A more important advantage is that we
can increase the accuracy of the resulting population estimates by using appropriately defined strata.
a.
True
b.
False
12. Ideally, we prefer estimates that have large standard errors.
a.
True
b.
False
13. The sampling distribution of the mean will have the same standard deviation as the original population from which the
samples were drawn.
a.
True
b.
False
14. The Central Limit Theorem (CLT) says that as long as the sample size is reasonably large, there is about a 95%
chance that the magnitude of the sampling error for the mean will be no more than two standard errors.
a.
True
b.
False
15. A list of all members of the population from which we can choose a sample is called a frame, and the potential sample
members are called sampling units.
a.
True
b.
False
16. Simple random samples are typically used in real applications.
a.
True
b.
False
17. In stratified sampling with proportional sample sizes, the proportion of each stratum selected differs from stratum to
stratum.
a.
True
b.
False
18. Cluster sampling is often less convenient and more costly than other random sampling methods.
a.
True
b.
False
19. An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of
the population parameter being estimated.
a.
True
b.
False
Name:
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20. In systematic sampling, one of the first k members is selected randomly, and then every kth member after this one is
selected. The value k is called the sampling interval and equals the ratio N / n, where N is the population size and n is the
desired sample size.
a.
True
b.
False
21. The primary advantage of cluster sampling is sampling convenience (and possibly less cost). The downside, however,
is that the inferences drawn from a cluster sample can be less accurate, for a given sample size, than for other sampling
plans.
a.
True
b.
False
22. It is customary to approximate the standard error of the sample mean by substituting the sample standard
deviation s for in the formula: SE( ) = .
a.
True
b.
False
23. The averaging effect says that as you average more and more observations from a given distribution, the variance of
the average increases.
a.
True
b.
False
24. The standard error of an estimate is the standard deviation of the sampling distribution of the estimate. It measures
how much estimates from different samples vary.
a.
True
b.
False
25. The randomized response technique is a way of getting at sensitive information to avoid estimation errors due to
nontruthful responses.
a.
True
b.
False
26. Estimation is the process of inferring the value of an unknown population parameter using data from a random sample
a.
True
b.
False
27. An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population
parameter being estimated.
a.
True
b.
False
28. A confidence interval is an interval calculated from the population data, where we strongly believe the true value of the
population parameter lies.
a.
True
b.
False
29. The sampling distribution of the mean will have the same mean as the original population from which the samples
were drawn.
Name:
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a.
True
b.
False
30. The Central Limit Theorem (CLT) states that the sampling distribution of the mean is approximately normal, no matter
what the distribution of the population, so long as the sample size is large enough.
a.
True
b.
False
31. Systematic sampling is generally similar to simple random sampling in its statistical properties.
a.
True
b.
False
32. When we sample less than 5% of the population, the finite population correction factor; fpc = , is used
to modify the formula for the standard error of the sample mean.
a.
True
b.
False
33. In stratified sampling, the population is divided into relatively homogeneous subsets called strata, and then random
samples are taken from each stratum.
a.
True
b.
False
34. If a simple random sample of size n is chosen from a population of size N, then each member of the population has
probability N / n of being chosen in the sample.
a.
True
b.
False
35. A sample of size 20 is selected at random from a population of size N. If the finite population correction factor is
0.9418, then N must be 169.
a.
True
b.
False
36. The sampling distribution of any point estimate (such as the sample mean or proportion) is the distribution of the point
estimates we would obtain from all possible samples of a given size drawn from the population.
a.
True
b.
False
37. A point estimate is a single numeric value, a “best guess” of a population parameter, calculated from the sample data.
a.
True
b.
False
38. The difference between the point estimate and the true value of the population parameter being estimated is called the
estimation error.
a.
True
b.
False
Indicate the answer choice that best completes the statement or answers the question.
Name:
Class:
Date:
39. The probability of being chosen in a simple random sample of size n from a population of size N is:
a.
1/N
b.
N – 1/n
c.
N/n
d.
n/N
40. With proportional sample sizes:
a.
The proportion of a stratum in the sample is independent of the proportion of that stratum in the population
b.
The proportion of a stratum in the sample is the same as the proportion of that stratum in the population
c.
The proportion of a stratum in the sample is greater than the proportion of that stratum in the population
d.
The proportion of a stratum in the sample is less than the proportion of that stratum in the population
41. When a portion of the sample does not respond to the survey, results.
a.
measurement error
b.
nonresponse bias
c.
sampling error
d.
systematic failure
e.
nonlinear error
42. The defining property of a simple random sample is that:
a.
every sample has the same chance of being chosen
b.
the easiest method to access samples are chosen
c.
the fewest samples are chosen
d.
every fourth subject is chosen as a sample
43. Which of the following is not a consideration when determining appropriate sample size?
a.
The cost of sampling
b.
The timely collection of the data
c.
Interviewer fatigue
d.
The likelihood of nonsampling error
44. A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is
called a(n)
a.
interval estimation
b.
point estimation
c.
simple random sample.
d.
statistic
45. The standard deviation of is usually called the
a.
standard error of the mean
b.
standard error of the sample
c.
standard error of the population
d.
randomized standard error
46. Potential sample members, called sampling units, are:
a.
people
b.
companies
c.
households
d.
All of these options
47. An unbiased estimator is a:
a.
sample statistic used to approximate a population parameter
b.
sample statistic, which has an expected value equal to the value of the population parameter
c.
sample statistic whose value is usually less than the population parameter
d.
standard error of the mean
Name:
Class:
Date:
48. Which of the following are reasons for why simple random sampling is used infrequently in real applications?
a.
Samples can be spread over a large geographic region
b.
Simple random sampling requires that all sampling units be identified prior to sampling
c.
Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the
population
d.
All of these options
49. Identifiable subpopulations within a population are called:
a.
clusters
b.
samples
c.
blocks
d.
strata
e.
None of these options
50. A judgmental sample is a sample in which the
a.
sampling units are chosen using a random number table
b.
quality of sampling units judged
c.
sampling units are chosen according to the sampler’s judgment
d.
sampling units are all biased and vocal about it
51. The approximate standard error of the sample mean is calculated as:
a.
b.
c.
d.
52. The theorem that states that the sampling distribution of the sample mean is approximately normal when the
sample size n is reasonably large is known as the:
a.
central limit theorem
b.
central tendency theorem
c.
simple random sample theorem
d.
point estimate theorem
53. The accuracy of the point estimate is measured by its:
a.
standard deviation
b.
standard error
c.
sampling error
d.
nonsampling error
54. If systematic sampling is chosen as the sampling technique, it is probably because:
a.
Systematic sampling has better statistical properties than simple random sampling
b.
Systematic sampling is more convenient
c.
Systematic sampling always results in more representative sampling than simple random sampling
d.
None of these options
55. The Central Limit Theorem (CLT) is generally valid for:
a.
n > 5
b.
n > 10
c.
n > 20
d.
n > 30
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e.
any size n
56. The approximate 95% confidence interval for a population mean is:
a.
b.
c.
d.
57. The key to using stratified sampling is:
a.
identifying the strata
b.
selecting the appropriate strata
c.
defining the strata
d.
randomizing the strata
58. The reason the Central Limit Theorem (CLT) is such an important result in statistics is because:
a.
The CLT allows us to assume that the population distribution is approximately normal, provided n is
reasonably large
b.
The CLT allows us to estimate the population mean without knowing the exact form of the population
distribution, provided n is reasonably large
c.
The CLT allows us to construct confidence intervals for the population mean without knowing the exact form of
the population distribution, provided n is reasonably large
d.
All of these options
59. A sample in which the sampling units are chosen from the population by means of a random mechanism is a
a.
probability sample
b.
judgmental sample
c.
stratified sample
d.
systematic sample
60. A list of all members of the population is called a:
a.
sampling unit
b.
probability sample
c.
frame
d.
relevant population
61. Selecting a random sample from each identifiable subgroup within a population is called:
a.
random sampling
b.
systematic sampling
c.
stratified sampling
d.
cluster sampling
e.
None of these options
62. Which of the following statements are correct?
a.
A point estimate is an estimate of the range of a population parameter
b.
A point estimate is a single value estimate of the value of a population parameter
c.
A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the
population standard deviation
d.
All of these options
63. Which of the following statements correctly describe estimation?
a.
It is the process of inferring the values of known population parameters from those of unknown sample
statistics.
b.
It is the process of inferring the values of unknown sample statistics from those of known population
Name:
Class:
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parameters.
c.
It is the process of inferring the values of known sample statistics from those of unknown population
parameters.
d.
It is the process of inferring the values of unknown population parameters from those of known sample
statistics.
64. Which of the following statements are correct?
a.
A confidence interval describes a range of values that is likely not to include the actual population parameter
b.
A confidence interval is an estimate of the range for a sample statistic.
c.
A confidence interval is an estimate of the range of possible values for a population parameter.
d.
None of these options
65. The opportunity for nonsampling error is increased by:
a.
larger sample sizes
b.
smaller sample sizes
c.
affluent samples
d.
educated samples
66. There is approximately % chance that any particular will be within two standard deviations of the population mean (
).
a.
90
b.
95
c.
99
d.
99.7
67. Sampling error is evident when:
a.
a question is poorly worded
b.
the sample is too small
c.
the sample is not random
d.
the sample mean differs from the population mean
68. Measurement error occurs when:
a.
a portion of the sample does not respond to the survey
b.
the sample responses are not clear
c.
the responses to question do not reflect what the investigator had in mind
d.
the investigator does not correctly tally all responses
69. Non-truthful response is a particular problem when:
a.
sensitive questions are asked.
b.
surveys are anonymous.
c.
interviewers are not trained.
d.
the sample is from an unusual population.
70. The sampling mean is the estimate for the population mean .
a.
random
b.
point
c.
simple
d.
interval
71. The opportunity for sampling error is decreased by:
a.
larger sample sizes
b.
smaller sample sizes
c.
affluent samples
d.
educated samples
72. The sampling method in which a population is divided into blocks and then selected by choosing a random
Name:
Class:
Date:
mechanism is called a
a.
random sampling
b.
systematic sampling
c.
stratified sampling
d.
cluster sampling
73. The finite population correction factor, , should generally be used when:
a.
N is any finite size
b.
n is less than 5% of the population size N
c.
n is greater than 5% of the population size N
d.
n is any finite size
74. A sampling error is the result of:
a.
measurement error
b.
nonresponse bias
c.
nontruthful responses
d.
bad luck
75. The mean of the sampling distribution of always equals
a.
the population mean
b.
/ n
c.
the population standard deviation
d.
/ n
76. In sampling, a population is:
a.
the set of all humans
b.
the set of all members about which a study intends to make inferences
c.
any group of test subjects
d.
a random group of individuals, households, cities or countries
77. The averaging effect means that as you average more and more observations from a given distribution, the variance
of the average
a.
increases
b.
decreases
c.
is unaffected
d.
could either increase, decrease or stay the same
78. The two basic sources for error when using random sampling are:
a.
sampling and selection
b.
identification and selection
c.
sampling and nonsampling
d.
bias and randomness
e.
linear and nonlinear
The manager of a small computer company has collected current annual salaries and number of years of post-secondary
education for 52 full-time employees. The data are shown below:
Current annual salaries:
Name:
Class:
Date:
Number of years of post-secondary education:
79. (A) Compute the mean, median, and standard deviation of the annual salaries for the 52 employees in the given
frame.
(B) Use Excel to choose a systematic sample of size 13 from the frame of annual salaries.
(C) Compute the mean, median, and standard deviation of the annual salaries for the 13 employees included in your
systematic sample in (B)
(D) Compare your statistics in (C) with your computed descriptive measures for the frame in (A). Is your systematic
sample representative of the frame with respect to the annual salary variable?
(E) Assume that we wish to stratify these employees by the number of years of post-secondary education, select such a
stratified sample of size 15 with approximately proportional sample sizes.
(F) Compute the mean, median, and standard deviation of the annual salaries for the 15 employees included in your
stratified sample in (E).
(G) Compare these statistics in (F) with your computed descriptive measures for the frame obtained in (A). Is your
stratified sample representative of the frame with respect to the annual salary variable?
Auditors of Old Kent Bank are interested in comparing the reported value of customer savings account balances with their
own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the
bank, the auditors decide to examine a representative sample of savings account balances. The frame from which they
will sample is shown below.
Name:
Class:
Date:
$75.30
$614.11
$696.34
$572.08
$748.23
$21.20
$99.79
$1,233.38
$530.40
$378.37
$596.14
$239.65
$2,995.38
$1,069.06
$929.80
$259.98
$123.65
$68.92
$192.35
$754.45
$309.00
$163.31
$71.75
$904.92
$40.70
$161.12
$459.38
$171.48
$402.81
$157.44
$41.81
$87.08
$489.97
$468.12
$400.57
$319.40
$533.82
$1,801.35
$1,666.50
$37.16
$85.92
$91.43
$193.14
$106.95
$214.62
$10.62
$582.18
$39.65
$123.66
$76.33
$291.73
$398.48
$659.18
$101.24
$1,740.47
$322.26
$1,509.34
$1,599.04
$358.62
$492.05
$1,052.68
$596.33
$100.54
$1,288.70
$421.46
$1,799.51
$581.21
$571.63
$180.58
$98.82
$358.68
$38.93
$874.78
$2,761.93
$750.44
$376.60
$269.48
$456.79
$216.81
$305.49
80. (A) What sample size would be required for the auditors to be approximately 95% sure that their estimate of the
average savings account balance at this bank is within $150 of the true mean? Assume that their best estimate of the
population standard deviation is $300.
(B) Choose a simple random sample of the size found in (A).
(C) Compute the observed sampling error based on the sample you have drawn from the population. How
does the actual sampling error compare to the maximum possible probable absolute error established in (A)?
Explain
A university bookstore manager is mildly concerned about the number of textbooks that were under-ordered and thus
unavailable two days after the beginning of classes. The manager instructs an employee to pick a random number, go to
the place where that number book is shelved, examine the next 50 titles, and record how many titles are unavailable.
81. (A) Technically, this process does not yield a random sample of the books in the store. Why not?
(B) How could a truly random sample be obtained?
An editor of a local newspaper is concerned with the number of errors that are found in the daily paper. In order to
understand the extent of this problem, the editor would like to estimate the average number of errors in the daily paper.
The frame in this case is the number of errors found in the daily paper for the past six months (180 issues).
82. (A) What sample size would be required for the production personnel to be approximately 95% sure that their estimate
of the average number of errors per issue is within 4 errors of the true mean? Assume that the editor’s best estimate of
the population standard deviation ( ) is 10 errors per issue.
(B) How does your answer to (A) change if the editor wants the estimate to be within 3 errors of the actual
population mean? Explain the difference in your answers to (A) and (B).
83. A cannery claims that its sardine cans have a net weight of 8 oz., with a standard deviation of 0.1 oz. You take a
simple random sample of 30 cans and encounter a sample mean of 7.85 oz. Are you inclined to believe the claim?
Name:
Class:
Date:
A battery manufacturer wants to estimate the average number of defective (or dead) batteries contained in a box shipped
by the company. Production personnel at this company have recorded the number of defective batteries found in each of
the 2000 boxes shipped in the past week.
84. (A) What sample size would be required for the production personnel to be approximately 95% sure that their estimate
of the average number of defective batteries per box is within 0.3 unit of the true mean? Assume that the best estimate of
the population standard deviation ( ) is 0.9 defective batteries per box.
(B) How does your answer to (A) change if the production personnel want their estimate to be within 0.5 unit of
the actual population mean? Evaluate the tradeoff between required accuracy and sample size requirement for
this case and the case in (A).
Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the
standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at
random.
85. (A) Find the mean and standard deviation of the sampling distribution of the average weekly earnings in the sample.
(B) Find probability that the mean of the sample is less than $445.
(C) Find the probability that the mean of the sample is between $445 and $455.
(D) Find the probability that the mean of the sample is greater than $460.
(E) Explain why the assumption of normality about the distribution of the average weekly earnings for employees was not
involved in the answers to (A) through (D).
A columnist for the LA Times is working to meet a deadline on a story about commuting in Los Angeles. She wants to
include information about the current price of gasoline in the Los Angeles metro area, but her source person for this type
of information has already gone home for the day. So she decides to take her own sample as she drives home, writing
down the prices she observes as she makes her way from downtown to her neighborhood in the suburbs. Below is the
data sample she obtains (units are $/gallon).
86. (A) Do you think she has obtained a true random sample?
(B) What average price could she report, based on the above sample?
(C) What average price range could she report, based on the above sample?
(D) Do you see any issues with reporting the range calculated for (C)?
The manager of a local fast–food restaurant is interested in improving service provided to customers who use the
restaurant’s drive-up window. As a first step in the process, the manager asks his assistant to record the time (in minutes)
it takes to serve a large number of customers at the final window in the facility’s drive-up system. The given frame in this
case is 200 customer service times observed during the busiest hour of the day for this fast-food restaurant. The frame of
200 service times yielded a mean of 0.881. A simple random sample of 10 from this frame is presented below.
Name:
Class:
Date:
Customer
1
2
3
4
5
6
7
8
9
10
Service time
1.02
1.18
0.95
0.90
0.85
1.10
0.75
0.60
1.25
1.00
87. (A) Compute the point estimate of the population mean from the sample above. What is the sampling error in this
case? Assume that the population consists of the given 200 customer service times.
(B) Compute the point estimate of the population standard deviation from the sample above.
(C) Should you use the finite population correction (fpc) factor to estimate the standard error of ? Explain. If your
answer is yes, what is the value of the fpc?
(D) Determine a good approximation to the standard error of the mean in this case.
A statistics professor has just given the final examination in his introductory statistics course. In particular, he is interested
in learning how his class of 50 students performed on this exam. The data are shown below.
78
72
73
75
79
72
75
77
71
78
83
84
71
81
82
79
71
73
89
74
75
93
74
88
83
90
82
79
62
73
88
76
76
76
80
84
84
91
70
76
74
68
80
87
92
84
79
80
91
74
88. (A) Using these 50 students as the frame, use Excel to generate a simple random sample of size 10 from this frame.
(B) Compute the mean scores in the frame and the simple random sample you generated in (A).
(C) Compare the mean scores you computed in (B). Is your simple random sample a good representative of the frame?
Why or why not?
(D) Using these 50 students as the frame, use Excel to generate a systematic sample of size 10 from this frame.
(E) Compare the mean scores in the frame with that in the systematic sample in (D). What do you conclude?
89. Consider the frame of 50 full-time employees of Computer Technologies, Inc (CTI). CTI’s human resources manager
has collected annual salary figures for all employees and she has calculated a mean of $47,723, a median of $41,082 and
a standard deviation of $24,167. A simple random sample of 10 employees is presented below (salary is in $1,000’s).
Compute the mean, median, and standard deviation for the sample and compare these statistics with the measures for
the entire company.
Employee
1
2
3
4
5
6
7
8
9
10
Salary
38.8
46.7
61.1
49.6
58.5
78.8
36.7
46.5
47.6
56.7
90. A sales manager for a company that makes commercial ovens for restaurants is interested in estimating the average
number of restaurants in all metropolitan areas across the entire country. He does not have access to the data for each
metropolitan location, so he had decided to select a sample that will be representative of all such areas, and will use a
sample size of 30. Do you believe that simple random sampling is the best approach to obtaining a representative subset
of the metropolitan areas in the given frame? Explain. If not, recommend how the sales manager might proceed to select
a better sample of size 30 from this data?
Sally Bird of Big Rapids Realty has received data on 60 houses that were recently sold in Mecosta County in Michigan.
The data are recorded in the table shown below. Included in this data set are observations for each of the following
variables:
Name:
Class:
Date:
· The appraised value of each house (in thousands of dollars)
· The selling price of each house (in thousands of dollars)
· The size of each house (in hundreds of square feet)
· The number of bedrooms in each house
91. (A) Suppose that Sally wishes to examine a representative subset of these 60 houses that has been stratified by the
number of bedrooms. Use Excel to assist her by finding such a stratified sample of size 10 with proportional sample sizes.
(B) Explain how Sally could apply cluster sampling in selecting a sample of size 15 from this frame.
(C) What are the advantages and disadvantages of employing cluster sampling in this case?
Suppose that you are an entrepreneur interested in establishing a new Internet-based auction service. Furthermore,
suppose that you have gathered basic demographic information on a large number of Internet users. You currently have
information on 1000 individuals related to their gender, age, education, marital status, annual household income, and
number of people in household. Assume that these individuals were carefully selected through stratified sampling.
92. (A) To assess potential interest in your proposed enterprise, you would like to conduct telephone interviews with a
representative subset of the 1000 Internet users. How would you proceed to stratify the given frame of 1000 individuals to
choose 50 for telephone interviews? Explain your approach.
(B) Explain how you could apply cluster sampling to obtain a sample size of 50 from this frame. What are the advantages
and disadvantages of employing cluster sampling in this case?
Name:
Class:
Date:
Name:
Class:
Date:
Name:
Class:
Date:
Name:
Class:
Date:
$38,450
$109,285
$87,489
$49,638
$76,927
$90,473
$89,867
$28,743
$39,205
$54,199
$49,987
$21,750
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generated random numbers) to select 50 books to be examined.
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are very close. From this analysis, we can conclude that the systematic sample is fairly representative of the frame or
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deviation is much smaller (about 51%) of the population standard deviation.
areas across the country.
annual income groups that represent your customers. You may find that you have different responses between these
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drawn from this type of sample may not be representative of the entire population.