Chapter 21 – Sample Survey
MULTIPLE CHOICE
1. The target population and the sampled population
a.
are always the same
b.
are not always the same
c.
must be the same for the results to be accurate
d.
None of these alternatives is correct.
2. Conclusions drawn from a sample survey
a.
apply only to the sample
b.
apply to any population
c.
apply only to the sampled population
d.
None of these alternatives is correct.
3. A target population is
a.
the population from which the sample is actually selected
b.
the population for which inferences are to be made
c.
always the same as the sampled population
d.
the same as the sample
4. The entity on which data are collected is
a.
the sample
b.
the element
c.
the population
d.
termed a census
5. A number added to and subtracted from a point estimate to create an approximate 95% confidence
interval is known as
a.
cluster of points
b.
bound on sampling error
c.
area point estimation
d.
systematic sampling error
6. A survey of a subset of a population is called a
a.
sample survey
b.
target survey
c.
sampled population
d.
survey of element
7. The population from which the sample is actually selected is
a.
always the target population
b.
the census
c.
the selected sample
d.
the sampled population
8. The units that are selected for sampling constitute the
a.
sample
b.
population
c.
frame
d.
sampling unit
9. A survey of an entire population is called
a.
population analysis
b.
population
c.
census
d.
target population
10. A sampling unit
a.
must have one element
b.
may include several elements
c.
cannot include more than one element
d.
None of these alternatives is correct.
11. A list of the sampling units for a study is
a.
the sampled population
b.
called the frame
c.
the same as the sample
d.
the sample space
12. Probabilistic sampling is any method of sampling in which
a.
the probability of the occurrence of various events in the study are known
b.
there are only two possible outcomes, such as P(A) and P(Ac)
c.
the probability of each possible sample can be computed
d.
the probability of each possible sample is one
13. Any method of sampling for which the probability of selecting a sample cannot be computed is termed
a.
probability sampling
b.
nonprobabilistic sampling
c.
unknown population sampling
d.
None of these alternatives is correct.
14. Convenience sampling is an example of
a.
probabilistic sampling
b.
sampling where the probabilities are known
c.
nonprobabilistic sampling
d.
None of these alternatives is correct.
15. Which of the following is an example of nonprobabilistic sampling?
a.
simple random sampling
b.
stratified simple random sampling
c.
cluster sampling
d.
judgment sampling
16. The error that occurs because a sample, and not the entire population, is used to estimate a population
parameter is a
a.
nonsampling error
b.
sampling error
c.
judgment error
d.
standard error
17. A sample selected in such a manner that each sample of size n has the same probability of being
selected is
a.
a convenience sample
b.
a judgment sample
c.
nonprobabilistic sampling
d.
a simple random sample
18. Which of the following sampling methods is a probabilistic sampling method?
a.
judgment sampling
b.
convenience sampling
c.
cluster sampling
d.
None of these alternatives is correct.
19. Stratified random sampling is a method of selecting a sample in which
a.
the sample is first divided into strata, and then random samples are taken from each
stratum
b.
various strata are selected from the sample
c.
the population is first divided into strata, and then random samples are drawn from each
stratum
d.
None of these alternatives is correct.
20. Cluster sampling is
a.
a nonprobability sampling method
b.
the same as convenience sampling
c.
a probability sampling method
d.
None of these alternatives is correct.
21. A version of cluster sampling in which the elements are formed into clusters on the basis of their
geographic proximity is
a.
stratified simple random sampling
b.
random sampling
c.
judgment sampling
d.
area sampling
22. A method of selecting a sample by randomly selecting the first element and then selecting every kth
element thereafter is
a.
area sampling
b.
stratified sampling
c.
systematic sampling
d.
stratified simple random sampling
23. Which of the following is (are) the most common type(s) of surveys?
a.
only mail surveys
b.
only telephone surveys
c.
only personal interviews
d.
All of these answers are correct.
24. With nonprobabilistic sampling
a.
it is possible to make estimates about the precision of the population parameters
b.
it is not possible to make statements about the precision of estimates made concerning the
population parameters
c.
the precision can be estimated if the sample is larger than 30
d.
None of these alternatives is correct.
25. The advantage of nonprobabilistic sampling is that it is inexpensive and
a.
provides statistically valid statements about the precision of the estimate
b.
can provide valid parameter estimates
c.
is error free
d.
None of these alternatives is correct.
26. Errors such as measurement error, processing error, and interviewer error are
a.
sampling errors
b.
nonsampling errors
c.
could be either sampling or nonsampling errors
d.
impossible to detect
27. In a sample survey, it is common practice to use a t value of (when approximating a 95% confidence
interval)
a.
1
b.
2
c.
3
d.
4
28. Sampling errors can
a.
be avoided by increasing the sample size to at least 30
b.
be avoided if the sample is increased so that it will be at least 5% of the population
c.
be avoided by using probabilistic sampling
d.
not be avoided
29. An unbiased estimate of the population total is given by the
a.
sample mean multiplied by the size of the sample
b.
sample mean multiplied by the size of the population
c.
sample size multiplied by the standard error
d.
standard deviation divided by the square root of the sample size
Exhibit 21-1
A simple random sample of size 64 is taken from a population of size 800. The sample mean is
determined to be 2,550 with a standard deviation of 500.
30. Refer to Exhibit 21-1. The point estimate of the population total is
a.
51,200
b.
1,275,000
c.
102,000
d.
2,040,000
31. Refer to Exhibit 21-1. An estimate of the standard error of the mean (for the total) is
a.
62,500.50
b.
47,958.32
c.
7.8125
d.
50,000.00
Exhibit 21-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample
mean is 500, and the sample standard deviation is 60.
32. Refer to Exhibit 21-2. The standard error of the mean is
a.
9.2
b.
43.0
c.
1.6
d.
8.9
33. Refer to Exhibit 21-2. An approximate 95% confidence interval for the population mean is
a.
482.2 to 517.8
b.
440.0 to 560.0
c.
500.0 to 560.0
d.
440.0 to 500.0
34. Refer to Exhibit 21-2. The population total is
a.
34,400
b.
21,500
c.
400,000
d.
500,000
35. Refer to Exhibit 21-2. An approximate 95% confidence interval for the population total is
a.
482 to 517
b.
385,759 to 414,241
c.
400,000 to 500,000
d.
350,000 to 450,000
Exhibit 21-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400,
and the sample standard deviation is 40.
36. Refer to Exhibit 21-3. An estimate of the standard error of the mean is
a.
4.0
b.
5.0
c.
6.0
d.
7.0
37. Refer to Exhibit 21-3. An approximate 95% confidence interval for the population mean is
a.
395 to 405
b.
380 to 420
c.
360 to 440
d.
390 to 410
38. Refer to Exhibit 21-3. The population total is
a.
3,944
b.
16,000
c.
240,000
d.
24,000
39. Refer to Exhibit 21-3. An approximate 95% confidence interval for the population total is
a.
350,000 to 450,000
b.
234,010 to 245,990
c.
350 to 400
d.
390 to 409
Exhibit 21-4
Simple random sampling has been used to obtain a sample of size 50 from a population of size 500.
The sample proportion was 0.7.
40. Refer to Exhibit 21-4. The estimate of the standard error of proportion is
a.
0.210
b.
0.700
c.
0.300
d.
0.062
41. Refer to Exhibit 21-4. An approximate 95% confidence interval for the population proportion is
a.
0.500 to 0.700
b.
0.750 to 0.810
c.
0.576 to 0.824
d.
0.638 to 0.762
42. Survey costs are highest for
a.
mail surveys
b.
personal interview surveys
c.
Internet surveys
d.
telephone surveys
43. A list of the sampling units for a study is called a
a.
frame
b.
cluster
c.
stratum
d.
population
44. Not sampling from the intended target population is an example of
a.
stratified sampling
b.
sampling error
c.
cluster sampling
d.
nonsampling error
45. Selecting a subset of clusters and then collecting data on all elements in those clusters is referred to as
a.
stratified cluster sampling
b.
convenient cluster sampling
c.
single-stage cluster sampling
d.
two-stage cluster sampling
46. Selecting a subset of clusters and then selecting a sample of elements in each of those clusters is
referred to as
a.
stratified cluster sampling
b.
convenient cluster sampling
c.
single-stage cluster sampling
d.
two-stage cluster sampling
PROBLEM
1. Nancy Joon, Inc. has 1500 employees. A simple random sample of 81 employees was selected, and the
individuals in the sample were asked how much they contribute (monthly) to their retirement accounts.
The sample mean, , was $150 with a standard deviation, s, of $45.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
4.86 (rounded)
b.
$140.28 to $159.72
2. Simple random sampling has been used to obtain a sample of size 60 from a population of size 700.
The sample mean was 500 with a standard deviation of 60.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
7.4 (rounded)
b.
458.2 to 514.8
3. Assume simple random sampling has been used, and the following information was obtained.
Population size
Sample size
Sample mean
Sample standard deviation
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
11.76 (rounded)
b.
276.48 to 323.52
4. The accounting firm of Nancy Amari & Associates (NAA) was commissioned to audit a population of
500 accounts. For this audit, NAA selected a simple random sample of 64 accounts. The sample
showed an average discrepancy of $120 with a standard deviation of $24.
a.
Estimate the population total discrepancy.
b.
Develop an approximate 95% confidence interval for the population total discrepancy.
a.
$60,000
b.
$57,200 to $62,800
5. A university has 5,000 students. The manager of food services at the university is interested in
determining the total lunch expenditure. A simple random sample of 121 lunch receipts was selected.
The sample showed an average of $3 with a standard deviation of $0.40.
a.
Estimate the standard error of the sample mean.
b.
Develop an approximate 95% confidence interval for the population mean.
c.
Estimate the population’s total expenditure for lunch.
d.
Develop an approximate 95% confidence interval for the total expenditure for lunch.
a.
0.0359
b.
2.93 to 3.07 (rounded)
c.
15,000
d.
14,640.79 to 15, 359.21
6. A simple random sample of size 36 is selected from a population of size 750. The sample mean is 318,
and the sample standard deviation is found to be 30.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
a.
4.9 (rounded)
b.
308.2 to 327.8 (rounded)
7. A company has 600 employees. A random sample of 49 employees took a computer literacy test. The
sample resulted in a mean score of 75 with a standard deviation of 21.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean of the 600
employees.
a.
2.9 (rounded)
8. Simple random sampling has been used to obtain a sample of 81 elements from a population of size
500. The sample mean is 120, and the sample standard deviation is determined to be 36.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
c.
Estimate the population total.
d.
Develop an approximate 95% confidence interval for the population total.
a.
3.7 (rounded)
b.
112.68 to 127.32
c.
60,000
d.
56,338.3 to 63,661.7
9. From a population consisting of 8,000 elements, a sample of size 121 is selected. The sample has a
mean of 4,000 and a standard deviation of 600.
a.
Estimate the standard error of the mean.
b.
Develop an approximate 95% confidence interval for the population mean.
c.
Estimate the population total.
d.
Develop an approximate 95% confidence interval for the population total.
a.
54.1
b.
3,891.7 to 4,108.3
c.
32,000,000
d.
31,133,898 to 32,866,102
10. A random sample of 60 elements was selected from a population of size 400. The sample proportion
a.
Estimate the standard error of the proportion.
b.
Develop an approximate 95% confidence interval for the population proportion.
a.
0.052
b.
0.146 to 0.354
11. Simple random sampling has been used to obtain a sample of n = 40 elements from a population of
N=300. The sample proportion
b.
69.2 to 80.8 (rounded)
a.
Estimate the standard error of the proportion.
b.
Develop an approximate 95% confidence interval for the population proportion.
12. From a population of 2000 accounts receivable, a simple random sample of 120 accounts is selected.
Thirty-six of the accounts in the sample were overdue.
a.
Estimate the standard error of the proportion of the overdue accounts.
b.
Develop an approximate 95% confidence interval for the proportion of overdue accounts in the
population.
a.
0.041
b.
0.219 to 0.381
13. We are interested in selecting a sample from a population of size 4,000 in order to develop an
approximate 95% confidence interval estimate of the population mean. A pilot study has resulted in a
standard deviation of 600. What should be the sample size if we do not want the sampling error to
exceed 200?
14. A community has 2,000 registered voters. A pilot study revealed that 70% of the individuals are
planning to vote for the incumbent mayor. We are interested in selecting a sample. So that the
sampling error will not exceed 4%, what size sample should be taken?
15. A stratified simple random sample has been taken with the following results.
Stratum (h)
xh
Sh
Nh
nh
1
26
1.5
200
35
2
23
1.4
150
25
3
27
1.8
180
40
4
24
1.5
220
30
5
21
2.0
250
25
a.
Determine a point estimate for the mean of the population.
b.
Estimate the standard error of the mean.
a.
0.06
b.
0.681 to 0.919
c.
Approximate a 95% confidence interval for the population mean.
d.
Compute the population total.
e.
Determine a 95% confidence interval for the population total.
16. The following are the results provided by a stratified simple random sample.
Stratum (h)
xh
Sh
Nh
nh
1
500
30
170
50
2
300
60
150
30
3
400
80
180
40
a.
Determine a point estimate for the mean of the population.
b.
Estimate the standard error of the mean.
c.
Approximate a 95% confidence interval for the population mean.
d.
Compute the population total.
e.
Determine a 95% confidence interval for the population total.
a.
404
b.
5.12
c.
393.7 to 414.2
d.
202,000
e.
196,877.8 to 207,122.2
17. A stratified simple random sample has been taken with the following results.
Stratum (h)
ph
Nh
nh
1
0.25
400
30
2
0.30
350
45
3
0.35
250
40
a.
Determine the point estimator of the population proportion.
b.
Estimate the standard error of the population proportion.
c.
Develop an approximate 95% confidence interval for the population proportion.
a.
0.2925
b.
0.0421
c.
0.2083 to 0.3767
a.
24.04
b.
0.133
c.
23.77 to 24.31
d.
24,040
e.
23,773.4 to 24,306.6
18. The following are the results of a stratified random sample.
Stratum (h)
ph
Nh
nh
1
0.15
300
50
2
0.18
400
60
3
0.26
350
40
4
0.20
450
55
a.
Determine the point estimator of the population proportion.
b.
Estimate the standard error of the population proportion.
c.
Develop an approximate 95% confidence interval for the population proportion.
a.
0.1987
c.
0.1454 to 0.2519
19. A sample of 5 clusters is to be taken from a population with N = 30 clusters and M = 300 elements in
the population. The values of Mi and Xi for each cluster are shown below.
Cluster
Mi
Xi
1
24
200
2
16
300
3
20
400
4
12
350
5
28
450
Total
100
1,700
a.
Determine the point estimate of the population mean.
b.
Determine the standard error of the mean.
c.
Develop a 95% confidence interval for the population mean.
d.
Determine the point estimator of the population total.
e.
Approximate a 95% confidence interval estimate of the population total.
a.
17
b.
5.39
c.
6.22 to 27.77
d.
5100
e.
1868 to 8332
20. A sample of 4 clusters is to be taken from a population with N = 50 clusters and M = 800 elements in
the population. The values of Mi and Xi for each cluster are shown below.
Cluster
Mi
Xi
1
8
70
2
14
120
3
16
80
4
12
130
Total
50
400
a.
Determine the point estimate of the population mean.
b.
Determine the standard error of the mean.
c.
Develop a 95% confidence interval for the population mean.
d.
Determine the point estimator of the population total.
e.
Approximate a 95% confidence interval estimate of the population total.
21. A sample of 5 clusters is to be taken from a population with N = 30 clusters and M = 420 clusters in
the population. The values of Mi and ai are shown below.
Cluster
Mi
ai
1
10
3
2
18
2
3
12
1
4
11
5
5
9
1
Total
60
12
a.
Determine the point estimator of the population proportion.
b.
Determine an approximate 95% confidence interval estimate for the population proportion.
a.
0.20
b.
0.0909 to 0.3091
22. A sample of 4 clusters is to be taken from a population with N = 40 clusters and M = 600 clusters in
the population. The values of Mi and ai are given below.
Cluster
Mi
ai
1
15
1
2
12
3
3
13
2
4
10
5
Total
50
11
a.
Determine the point estimator of the population proportion.
b.
Determine an approximate 95% confidence interval estimate for the population proportion.
a.
8
b.
1.03
c.
5.93 to 10.06
d.
826.03