Chapter 7 – Sampling and Sampling Distributions
Multiple Choice
1. The expected value of equals the mean of the population from which the sample is drawn
a.
only if the sample size is 30 or greater
b.
only if the sample size is 50 or greater
c.
only if the sample size is 100 or greater
d.
for any sample size
2. The basis for using a normal probability distribution to approximate the sampling distribution of is
a.
Chebyshev’s theorem
b.
the empirical rule
c.
the central limit theorem
d.
Bayes’ theorem
c
3. The standard deviation of is referred to as the
a.
b.
c.
d.
4. The standard deviation of is referred to as the
a.
standard x
b.
standard error of the mean
c.
sample standard mean
d.
sample mean deviation
5. The value of the ___________ is used to estimate the value of the population parameter.
a.
population statistic
b.
sample parameter
c.
population estimate
d.
sample statistic
6. The population being studied is usually considered ______ if it involves an ongoing process that makes listing or
counting every element in the population impossible.
a.
finite
Chapter 7 – Sampling and Sampling Distributions
b.
infinite
c.
skewed
d.
symmetric
7. A probability sampling method in which we randomly select one of the first k elements and then select every kth
element thereafter is
a.
stratified random sampling
b.
cluster sampling
c.
systematic sampling
d.
convenience sampling
c
8. The standard deviation of a point estimator is the
a.
standard error
b.
sample statistic
c.
point estimate
d.
sampling error
a
9. The finite correction factor should be used in the computation of when n/N is greater than
a.
.01
b.
.025
c.
.05
d.
.10
c
10. The set of all elements of interest in a study is
a.
set notation
b.
a set of interest
c.
a sample
d.
a population
11. A subset of a population selected to represent the population is a
a.
subset
b.
sample
c.
small population
d.
None of the alternative answers is correct.
Chapter 7 – Sampling and Sampling Distributions
b
1
12. The purpose of statistical inference is to provide information about the
a.
sample based upon information contained in the population
b.
population based upon information contained in the sample
c.
population based upon information contained in the population
d.
mean of the sample based upon the mean of the population
b
1
13. A simple random sample of size n from a finite population of size N is a sample selected such that each possible
sample of size
a.
N has the same probability of being selected
b.
n has a probability of 0.5 of being selected
c.
n has a probability of 0.1 of being selected
d.
n has the same probability of being selected
d
1
14. The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is
a.
15
b.
10
c.
20
d.
125
b
1
15. There are 6 children in a family. The number of children defines a population. The number of simple random samples
of size 2 (without replacement) which are possible equals
a.
12
b.
15
c.
3
d.
16
b
1
16. How many different samples of size 3 (without replacement) can be taken from a finite population of size 10?
a.
30
b.
1,000
c.
720
d.
120
1
17. A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that
can be selected from this population is
a.
24
b.
56
c.
512
d.
128
18. A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population.
On the first selection, the probability of an element being selected is
a.
0.100
b.
0.010
c.
0.001
d.
0.002
19. Excel’s RAND function
a.
determines sample size
b.
selects a simple random sample
c.
randomizes a population
d.
generates random numbers
20. A simple random sample of size n from a finite population of size N is to be selected. Each possible sample should
have
a.
the same probability of being selected
b.
a probability of 1/n of being selected
c.
a probability of 1/N of being selected
d.
a probability of N/n of being selected
a
21. A simple random sample from a process (an infinite population) is a sample selected such that
a.
each element selected comes from the same population
b.
each element is selected independently
c.
each element selected comes from the same population and each element is selected independently
d.
the probability of being selected changes
c
22. A numerical measure from a population, such as a population mean, is called
a.
a statistic
Chapter 7 – Sampling and Sampling Distributions
b.
a parameter
c.
a sample
d.
the mean deviation
23. A numerical measure from a sample, such as a sample mean, is known as
a.
a statistic
b.
a parameter
c.
the mean deviation
d.
the central limit theorem
a
24. A sample statistic, such as , that estimates the value of the corresponding population parameter is known as a
a.
point estimator
b.
parameter
c.
population parameter
d.
Both a parameter and a population parameter are correct.
a
25. A single numerical value used as an estimate of a population parameter is known as
a.
a parameter
b.
a population parameter
c.
both a parameter or a population parameter are correct
d.
a point estimate
26. In point estimation, data from the
a.
population is used to estimate the population parameter
b.
sample is used to estimate the population parameter
c.
sample is used to estimate the sample statistic
d.
None of the alternative ANSWERS is correct.
27. The sample mean is the point estimator of
a.
μ
b.
σ
c.
d.
a
28. The sample statistic s is the point estimator of
a.
μ
b.
σ
c.
d.
ANSWER:
b
POINTS:
1
29. Which of the following is(are) point estimator(s)?
a.
σ
b.
μ
c.
s
d.
All of these answers are correct.
ANSWER:
c
POINTS:
1
30. A simple random sample of 5 observations from a population containing 400 elements was taken, and the following
values were obtained.
12
18
19
20
21
A point estimate of the population mean is
a.
5
b.
18
c.
19
d.
20
ANSWER:
b
POINTS:
1
31. A probability distribution for all possible values of a sample statistic is known as a
a.
sample statistic
b.
parameter
c.
simple random sample
d.
sampling distribution
ANSWER:
d
POINTS:
1
32. A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is
a
a.
population parameter
b.
point estimator
c.
sample parameter
d.
point estimate
ANSWER:
d
POINTS:
1
33. If we consider the simple random sampling process as an experiment, the sample mean is
a.
always zero
b.
always smaller than the population mean
c.
a random variable
d.
exactly equal to the population mean
34. The probability distribution of all possible values of the sample mean is called the
a.
central probability distribution
b.
sampling distribution of the sample mean
c.
random variation
d.
standard error
35. The sampling distribution of the sample mean
a.
is the probability distribution showing all possible values of the sample mean
b.
is used as a point estimator of the population mean μ
c.
is an unbiased estimator
d.
shows the distribution of all possible values of μ
36. Since the sample size is always smaller than the size of the population, the sample mean must
a.
always be smaller than the population mean
b.
be larger than the population mean
c.
be equal to the population mean
d.
None of the alternative ANSWERS is correct.
37. The expected value of the random variable is
a.
σ
b.
the standard error
c.
the sample size
d.
μ
38. The standard deviation of all possible values is called the
a.
standard error of proportion
b.
standard error of the mean
Chapter 7 – Sampling and Sampling Distributions
c.
mean deviation
d.
central variation
b
1
39. In computing the standard error of the mean, the finite population correction factor is not used when
a.
n/N > 0.05
b.
N/n ≤ 0.05
c.
n/N ≤ 0.05
d.
n ≥ 30
c
1
40. A finite population correction factor is needed in computing the standard deviation of the sampling distribution of
sample means
a.
whenever the population is infinite
b.
whenever the sample size is more than 5% of the population size
c.
whenever the sample size is less than 5% of the population size
d.
The correction factor is not necessary if the population has a normal distribution
b
1
41. From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is
determined that the sample mean is 56. The standard error of the mean is
a.
3
b.
2
c.
greater than 2
d.
less than 2
d
1
42. From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the
population is 900. The standard error of the mean is approximately
a.
1.1022
b.
2
c.
30
d.
1.4847
d
1
43. A simple random sample of 64 observations was taken from a large population. The population standard deviation is
120. The sample mean was determined to be 320. The standard error of the mean is
a.
1.875
b.
40
c.
5
Chapter 7 – Sampling and Sampling Distributions
d.
15
44. As the sample size increases, the
a.
standard deviation of the population decreases
b.
population mean increases
c.
standard error of the mean decreases
d.
standard error of the mean increases
c
45. As the sample size increases, the variability among the sample means
a.
increases
b.
decreases
c.
remains the same
d.
depends upon the specific population being sampled
46. Doubling the size of the sample will
a.
reduce the standard error of the mean to one-half its current value
b.
reduce the standard error of the mean to approximately 70% of its current value
c.
have no effect on the standard error of the mean
d.
double the standard error of the mean
47. Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196.
The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are
a.
180 and 24.39
b.
180 and 28
c.
180 and 1.74
d.
180 and 2
c
48. Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are
200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the
distribution of sample means are
a.
200 and 18
b.
81 and 18
c.
9 and 2
d.
200 and 2
49. Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are
20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution
of sample mean are
a.
36 and 15
b.
20 and 15
c.
20 and 0.417
d.
20 and 2.5
50. 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 the
a.
approximation theorem
b.
normal probability theorem
c.
central limit theorem
d.
central normality theorem
51. The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution
whenever the sample size is large is based on the
a.
central limit theorem
b.
fact that there are tables of areas for the normal distribution
c.
assumption that the population has a normal distribution
d.
All of these answers are correct.
52. As the sample size becomes larger, the sampling distribution of the sample mean approaches a
a.
binomial distribution
b.
Poisson distribution
c.
hypergeometric distribution
d.
None of the alternative answers is correct.
53. Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability
distribution for
a.
only large sample sizes
b.
only small sample sizes
c.
any sample size
d.
only samples of size thirty or greater
54. For a population with an unknown distribution, the form of the sampling distribution of the sample mean is
a.
approximately normal for all sample sizes
b.
exactly normal for large sample sizes
c.
exactly normal for all sample sizes
d.
approximately normal for large sample sizes
55. A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
a.
approximately normal because is always approximately normally distributed
b.
approximately normal because the sample size is large in comparison to the population size
c.
approximately normal because of the central limit theorem
d.
normal if the population is normally distributed
56. A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of is
approximately normal because
a.
is always approximately normally distributed
b.
the sample size is small in comparison to the population size
c.
of the central limit theorem
d.
None of the alternative answers is correct.
57. A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The
probability that the mean from that sample will be larger than 82 is
a.
0.5228
b.
0.9772
c.
0.4772
d.
0.0228
58. A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The
probability that the mean from that sample will be between 183 and 186 is
a.
0.1359
b.
0.8185
c.
0.3413
d.
0.4772
a
59. A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The
Chapter 7 – Sampling and Sampling Distributions
probability that the sample mean will be between 80.54 and 88.9 is
a.
0.0347
b.
0.7200
c.
0.9511
d.
None of the alternative answers is correct.
c
1
60. A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The
probability that the sample mean will be greater than 57.95 is
a.
0
b.
.0495
c.
.4505
d.
None of the alternative answers is correct.
b
1
Exhibit 7-1
The following data was collected from a simple random sample from a process (an infinite population).
13
15
14
16
12
61. Refer to Exhibit 7-1. The point estimate of the population mean
a.
is 5
b.
is 14
c.
is 4
d.
cannot be determined because the population is infinite
b
1
62. Refer to Exhibit 7-1. The point estimate of the population standard deviation is
a.
2.500
b.
1.581
c.
2.000
d.
1.414
b
1
63. Refer to Exhibit 7-1. The mean of the population
a.
is 14
b.
is 15
c.
is 15.1581
d.
could be any value
d
1
Chapter 7 – Sampling and Sampling Distributions
Exhibit 7-2
Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said
“yes,” and one hundred said “no.”
64. Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond “yes” is
a.
300
b.
approximately 300
c.
0.75
d.
0.25
c
65. Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond “no” is
a.
75
b.
0.25
c.
0.75
d.
0.50
Exhibit 7-3
The following information was collected from a simple random sample of a population.
16
19
18
17
20
18
66. Refer to Exhibit 7-3. The point estimate of the mean of the population is
a.
18.0
b.
19.6
c.
108
d.
sixteen, since 16 is the smallest value in the sample
a
67. Refer to Exhibit 7-3. The point estimate of the population standard deviation is
a.
2.000
b.
1.291
c.
1.414
d.
1.667
c
Exhibit 7-4
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard
deviation of the contents (i.e., of the population) is 0.22 ounces.
68. Refer to Exhibit 7-4. The standard error of the mean equals
a.
0.3636
b.
0.0331
Chapter 7 – Sampling and Sampling Distributions
c.
0.0200
d.
4.000
c
1
69. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is
a.
0.22
b.
4
c.
121
d.
0.02
b
1
70. Refer to Exhibit 7-4. In this problem the 0.22 is
a.
a parameter
b.
a statistic
c.
the standard error of the mean
d.
the average content of colognes in the long run
a
1
Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of
8.
71. Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are
a.
8.7 and 1.94
b.
36 and 1.94
c.
36 and 1.86
d.
36 and 8
c
1
72. Refer to Exhibit 7-5. Which of the following best describes the form of the sampling distribution of the sample mean
for this situation?
a.
Approximately normal because the sample size is small relative to the population size.
b.
Approximately normal because of the central limit theorem.
c.
exactly normal
d.
None of the alternative answers is correct.
d
1
73. The probability distribution of all possible values of the sample proportion is the
a.
probability density function of
b.
sampling distribution of
Chapter 7 – Sampling and Sampling Distributions
c.
same as , since it considers all possible values of the sample proportion
d.
sampling distribution of
74. Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The
standard deviation of the sample proportions (i.e., the standard error of the proportion) is
a.
0.0004
b.
0.2100
c.
0.3000
d.
0.0200
75. A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were
females. The standard error of the proportion of females is
a.
0.0016
b.
0.2400
c.
0.1600
d.
0.0400
76. A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample
proportion for samples of size 100 are
a.
500 and 0.047
b.
500 and 0.050
c.
0.5 and 0.047
d.
0.5 and 0.050
c
77. Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The
mean and standard deviation of the distribution of sample proportions are
a.
0.2 and .04
b.
0.2 and 0.2
c.
20 and .04
d.
None of the alternative answers is correct.
a
78. As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability
distribution whenever
a.
np ≥ 5
b.
n(1 − p) ≥ 5