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7-1
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 07
Sampling and Sampling Distributions
True / False Questions
1. If we have a sample size of 100 and the estimate of the population proportion is .10, we can
estimate the sampling distribution of with a normal distribution.
True False
2. A sample size of 500 is sufficiently large to conclude that the sampling distribution of is a
normal distribution, when the estimate of the population proportion is .995.
True False
3. The sampling distribution of must be a normal distribution with mean = 0 and standard
deviation = 1.
True False
4. For any sampled population, the population of all sample means is approximately normally
distributed.
True False
5. The sampling distribution of a sample statistic is the probability distribution of the population
of all possible values of the sample statistic.
True False
6. A sample statistic is an unbiased point estimate of a population parameter if the mean of the
populations of all possible values of the sample statistic equals the population parameter.
True False

7-2
7. A minimum variance, unbiased point estimate has a variance that is as small as or smaller
than the variances of any other unbiased point estimate.
True False
8. We can randomly select a sample from an infinite population of potential process
measurements by sampling the process at different and equally spaced time points.
True False
9. The reason sample variance has a divisor of n - 1 rather than n is that it makes the variance
an unbiased estimate of the population variance.
True False
10. The standard deviation of all possible sample proportions increases as the sample size
increases.
True False
11. The Central Limit Theorem states that as sample size increases, the population distribution
more closely approximates a normal distribution.
True False
12. If a population is known to be normally distributed, then it follows that the sample standard
deviation must equal σ.
True False
13. If the sampled population is exactly normally distributed, then the sampling distribution of
is also expected to be normal, regardless of the sample size.
True False

7-3
14. If a population is known to be normally distributed, then it follows that the sample mean must
equal the population mean.
True False
15. If p = .8 and n = 50, then we can conclude that the sampling distribution of is
approximately a normal distribution.
True False
16. If p = .9 and n = 40, then we can conclude that the sampling distribution of is
approximately a normal distribution.
True False
17. If the sampled population distribution is skewed, then in most cases the sampling distribution
of the mean can be approximated by the normal distribution if the sample size n is at least 30.
True False
18. In order to select a stratified random sample, we divide the population into overlapping groups
of similar elements.
True False
19. As the sample size increases, the standard deviation of the sampling distribution increases.
True False
20. The standard deviation of the sampling distribution of the sample mean is σ.
True False
21. The mean of the sampling distribution of is always equal to the mean of the sampled
population.
True False

7-4
22. The sampling distribution of the sample mean is developed by repeatedly taking samples of
size n and computing the sample means and reporting the resulting sample means in the form
of a probability distribution.
True False
23. If the sample size n is infinitely large, then s2
is an unbiased estimator of σ2
.
True False
24. The sample standard deviation s is an unbiased estimator of the population standard
deviation σ.
True False
25. A common practice in selecting a sample from a large geographic area is multistage cluster
sampling.
True False
26. A low response rate has no effect on the validity of a survey's findings.
True False
27. Selecting a random sample is the only way to ensure that the information reflects the true
population.
True False
28. In random sampling without replacement, each element in the sample will be different.
True False
29. The quantity √(N - n)(N - 1) is called the finite population multiplier.
True False

7-5
30. There is no easy way to calculate an unbiased point estimate of σ.
True False
31. Stratification can at times be combined with multistage cluster sampling to develop an
appropriate sample.
True False
32. In systematic sampling, the first element is randomly selected from the first (N/n) elements.
True False
33. Sampling error occurs because of incomplete information.
True False
34. The target population is the result of sampling from the original population that is of interest
to the researcher.
True False
35. Errors of nonobservation occur when data values are recorded incorrectly.
True False
36. A recording error is an error of observation.
True False
Multiple Choice Questions

7-6
37. Which of the following is a type of question used in survey research?
A. Dichotomous
B. Free response
C. Rating
D. All of these
38. Methods for obtaining a sample are called:
A. Sample surveys.
B. Probability sampling.
C. Random sampling.
D. Sampling designs.
39. Nonoverlapping groups in random sampling of a population are called:
A. Clusters.
B. A frame.
C. Strata.
D. Stages.
40. When we perform ______________, an element of a population always has a chance of being
chosen at each point of selection.
A. Stratified random sampling
B. Sampling with replacement
C. Sampling without replacement
D. Cluster sampling

7-7
41. __________ sampling is defined as sampling where we know the chance that each element in
the population will be included in the sample.
A. Judgment
B. Convenience
C. Nonrandom
D. Probability
42. A "Yes or No" question is _____________.
A. Dichotomous
B. Multiple choice
C. Open-ended
D. Systematic
43. _____________ occurs when some population elements are excluded from the process of
selecting the sample.
A. Nonresponse
B. An error of observation
C. Undercoverage
D. Sampling error
44. _____________ is the difference between a numerical description of the population and the
corresponding descriptor of the sample.
A. Sampling error
B. Nonobservation error
C. Observation error
D. Nonresponse

7-8
45. The Central Limit Theorem states that as the sample size increases, the distribution of the
sample ____________ approaches the normal distribution.
A. Medians
B. Means
C. Standard deviations
D. Variances
46. Consider two population distributions labeled A and B. Distribution A is highly skewed and
nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling
distributions of A and B to achieve the same degree of normality:
A. Population A will require a larger sample size.
B. Population B will require a larger sample size.
C. Populations A and B will require the same sample size.
D. None of these.
47. As the sample size ______________, the variation of the sampling distribution of
___________.
A. Decreases, decreases
B. Increases, remains the same
C. Decreases, remains the same
D. Increases, decreases
E. None of these
48. Consider a sampling distribution formed based on n = 3. The standard deviation of the
population of all sample means is ______________ less than the standard deviation of the
population of individual measurements σ.
A. Always
B. Sometimes
C. Never

7-9
49. If the sampled population has a mean of 48 and standard deviation of 16, then the mean and
the standard deviation for the sampling distribution of for n = 16 are:
A. 4 and 1.
B. 12 and 4.
C. 48 and 4.
D. 48 and 1.
E. 48 and 16.
50. The population of all sample proportions has a normal distribution if the sample size (n) is
sufficiently large. The rule of thumb for ensuring that n is sufficiently large is:
A. np ≥ 5
B. n(1 - p) ≥ 5
C. np ≤ 5
D. n(1 - p) ≤ 5 and np ≤ 5
E. np ≥ 5 and n(1 - p) ≥ 5
51. Whenever the population has a normal distribution, the sampling distribution of is normal
or near normal distribution:
A. For only large sample sizes.
B. For only small sample sizes.
C. For any sample size.
D. For only samples of size 30 or more.
52. If a population distribution is known to be normal, then it follows that:
A. The sample mean must equal the population mean.
B. The sample mean must equal the population mean for large samples.
C. The sample standard deviation must equal the population standard deviation.
D. All of these.
E. None of these.

7-10
53. For nonnormal populations, as the sample size (n) ___________________, the distribution of
sample means approaches a(n) ________________ distribution.
A. Decreases, uniform
B. Increases, normal
C. Decreases, normal
D. Increases, uniform
E. Increases, exponential
54. The spread of the sampling distribution of is ____________ the spread of the corresponding
population distribution sampling distribution.
A. Larger than
B. Smaller than
C. The same as
D. Exactly ½
55. For large samples, the sampling distribution of is approximately normal with a mean of
_____.
A. μ
B. μ/√n
C.
D. z
56. ____________ says that if the sample size is sufficiently large, then the sample means are
approximately normally distributed.
A. Cluster sampling
B. Sampling error
C. Sampling distribution of the mean
D. The Central Limit Theorem

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7-11
57. According to the Central Limit Theorem, if a sample size is at least _____, then for most
sampled populations, we can conclude that the sample means are approximately normal.
A. 25
B. 20
C. 30
D. 50
58. If we wish to estimate a population parameter by using a sample statistic, we are using
___________.
A. Cluster sampling
B. Point estimation
C. Random sampling
D. Response bias
59. The mean of the sampling distribution of the sample proportion is equal to _____ when the
sample size is sufficiently large.
A. μ
B. p
C. p × n
D. (1 - p)
60. If the sampled population is finite and at least _____ times larger than the sample size, we
treat the population as infinite.
A. 5
B. 20
C. 30
D. 10

7-12
61. The notation for the standard deviation of the sampling distribution of the sample mean is
__________.
A.
B. σx
C.
D. μ
62. The sampling distribution of the sample mean is a normal distribution for ________ sample
sizes, regardless of the shape of the corresponding population distribution.
A. Random
B. Large
C. Larger than 50
D. Small
63. A theorem that allows us to use the normal probability distribution to approximate the
sampling distribution of sample means and sample proportions whenever the sample size is
large is known as _______________.
A. Cluster sampling
B. Sampling error
C. Sampling distribution of the mean
D. The Central Limit Theorem
64. As the sample size increases, the variability of the sampling distribution of the mean
______________.
A. Increases
B. Stays the same
C. Is variable
D. Decreases

7-13
65. As the sample size ___________, the standard deviation of the population of all sample
proportions increases.
A. Increases
B. Stays the same
C. Is variable
D. Decreases
66. The population of all _________________ proportions is described by the sampling distribution
of .
A. Population
B. Random
C. Observed
D. Sample
67. The ______________ of a sample statistic is the probability distribution of the population of all
possible values of the sample statistic.
A. Sample mean
B. Sampling distribution
C. Probability
D. Observations
68. The ___________ is a minimum-variance unbiased point estimate of the mean of a normally
distributed population.
A. Sample mean
B. Sample variance
C. Sample standard deviation
D. Observed mean

7-14
69. An unbiased estimate of σ2
is _____.
A. s
B. s2
C.
D. σ
70. A random sample of size 36 is taken from a population with a mean of 50 and a standard
deviation of 5. The sampling distribution of ____________________.
A. Cannot be determined
B. Is skewed to the left
C. Is approximately normal
D. Is skewed to the right
71. A random sample of size 1,000 is taken from a population where p = .20. Describe the
sampling distribution of .
A. Cannot be determined
B. Approximately normal
C. Skewed to the left
D. Skewed to the right
72.
Find if μ = 40, σx = 16, n = 16.
A. .9944
B. .4483
C. .5517
D. .1056

7-15
73. A PGA (Professional Golf Association) tournament organizer is attempting to determine
whether hole (pin) placement has a significant impact on the average number of strokes for
the 13th
hole on a given golf course. Historically, the pin has been placed in the front right
corner of the green, and the historical mean number of strokes for the hole has been 4.25,
with a standard deviation of 1.6 strokes. On a particular day during the most recent golf
tournament, the organizer placed the hole (pin) in the back left corner of the green. 64 golfers
played the hole with the new placement on that day. Determine the probability of the sample
average number of strokes exceeding 4.75.
A. .9938
B. .4013
C. .0062
D. .3783
74. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a
standard deviation of 0.2 ounces. The weights of the sugar packages are normally distributed.
What is the probability that 16 randomly selected packages will have a weight in excess of
16.075 ounces?
A. .0500
B. .3520
C. .9332
D. .0668
75. The population of lengths of aluminum-coated steel sheets is normally distributed with a
mean of 30.05 inches and a standard deviation of 0.3 inches. What is the probability that the
average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?
A. .8413
B. .6293
C. .3707
D. .1587

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