Chapter 8 – Interval Estimation
Multiple Choice
1. As the degrees of freedom increase, the t distribution approaches the
a.
uniform distribution
b.
normal distribution
c.
exponential distribution
d.
p distribution
2. If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals
a.
b.
c.
d.
3. The t distribution is a family of similar probability distributions, with each individual distribution depending on a
parameter known as the
a.
b.
c.
d.
4. The probability that the interval estimation procedure will generate an interval that does not contain the actual value of
the population parameter being estimated is the
a.
level of significance
b.
confidence level
c.
confidence coefficient
d.
error factor
5. To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except
a.
desired margin of error
b.
confidence level
c.
population standard deviation
d.
degrees of freedom
6. The use of the normal probability distribution as an approximation of the sampling distribution of is based on the
Chapter 8 – Interval Estimation
condition that both np and n(1 – p) equal or exceed
a.
.05
b.
5
c.
10
d.
30
b
1
7. The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed
using a planning value of p equal to
a.
.01
b.
.50
c.
.51
d.
.99
b
1
8. We can reduce the margin of error in an interval estimate of p by doing any of the following except
a.
increasing the sample size
b.
increasing the planning value p* to .5
c.
increasing the level of significance
d.
reducing the confidence coefficient
b
1
9. In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with
a.
degrees of freedom
b.
degrees of freedom
c.
n − 1 degrees of freedom
d.
n degrees of freedom
c
1
10. The expression used to compute an interval estimate of μ may depend on any of the following factors except
a.
the sample size
b.
whether the population standard deviation is known
c.
whether the population has an approximately normal distribution
d.
whether there is sampling error
d
1
11. The mean of the t distribution is
a.
0
b.
.5
Chapter 8 – Interval Estimation
c.
1
d.
problem specific
a
1
12. An interval estimate is used to estimate
a.
the shape of the population’s distribution
b.
the sampling distribution
c.
a sample statistic
d.
a population parameter
d
1
13. An estimate of a population parameter that provides an interval believed to contain the value of the parameter is
known as the
a.
confidence level
b.
interval estimate
c.
parameter value
d.
population estimate
b
1
14. As the sample size increases, the margin of error
a.
increases
b.
decreases
c.
stays the same
d.
None of the other answers are correct.
b
1
15. The confidence associated with an interval estimate is called the
a.
level of significance
b.
degree of association
c.
confidence level
d.
precision
c
1
16. The ability of an interval estimate to contain the value of the population parameter is described by the
a.
confidence level
b.
degrees of freedom
c.
precise value of the population mean μ
d.
None of the other answers are correct.
a
1
17. If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be
a.
0.1
b.
0.95
c.
0.9
d.
0.05
c
18. If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is
a.
0.485
b.
1.96
c.
0.95
d.
1.645
c
19. For the interval estimation of μ when σ is assumed known, the proper distribution to use is the
a.
standard normal distribution
b.
t distribution with n degrees of freedom
c.
t distribution with n − 1 degrees of freedom
d.
t distribution with n − 2 degrees of freedom
a
20. The z value for a 97.8% confidence interval estimation is
a.
2.02
b.
1.96
c.
2.00
d.
2.29
21. It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the
population. There is a .95 probability that the sample mean will provide a margin of error of
a.
7.84 or less
b.
31.36 or less
c.
344.96 or less
d.
1,936 or less
a
22. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard
deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is
a.
15.2 to 24.8
Chapter 8 – Interval Estimation
b.
19.2 to 20.8
c.
19.216 to 20.784
d.
21.2 to 22.8
Exhibit 8-1
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected
from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours.
23. Refer to Exhibit 8-1. The standard error of the mean is
a.
7.5
b.
0.014
c.
0.160
d.
0.133
24. Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately
a.
0.26
b.
1.96
c.
0.21
d.
1.64
a
25. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately
a.
7.04 to 110.96 hours
b.
7.36 to 10.64 hours
c.
7.80 to 10.20 hours
d.
8.74 to 9.26 hours
Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100
customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute.
26. Refer to Exhibit 8-2. The standard error of the mean equals
a.
0.001
b.
0.010
c.
0.100
d.
1.000
27. Refer to Exhibit 8-2. With a .95 probability, the sample mean will provide a margin of error of
Chapter 8 – Interval Estimation
a.
0.95
b.
0.10
c.
.196
d.
1.96
c
1
28. Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.80, the standard error of the mean
a.
will increase
b.
will decrease
c.
remains unchanged
d.
becomes negative
c
1
29. Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time of all customers is
a.
3 to 5
b.
1.36 to 4.64
c.
2.804 to 3.196
d.
1.04 to 4.96
c
1
Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The
distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.
30. Refer to Exhibit 8-3. If we are interested in determining an interval estimate for μ at 86.9% confidence, the z value to
use is
a.
1.96
b.
1.31
c.
1.51
d.
2.00
c
1
31. Refer to Exhibit 8-3. The value to use for the standard error of the mean is
a.
13.5
b.
9
c.
2.26
d.
1.5
d
1
32. Refer to Exhibit 8-3. The 86.9% confidence interval for μ is
a.
46.500 to 73.500
Chapter 8 – Interval Estimation
b.
57.735 to 62.265
c.
59.131 to 60.869
d.
50 to 70
33. Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for μ would
a.
not change
b.
become narrower
c.
become wider
d.
become zero
34. In general, higher confidence levels provide
a.
wider confidence intervals
b.
narrower confidence intervals
c.
a smaller standard error
d.
unbiased estimates
35. When the level of confidence increases, the confidence interval
a.
stays the same
b.
becomes wider
c.
becomes narrower
d.
cannot tell from the information given
36. A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is
reduced to 0.90, the interval for μ
a.
becomes narrower
b.
becomes wider
c.
does not change
d.
becomes 0.1
37. If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the
a.
width of the confidence interval to increase
b.
width of the confidence interval to decrease
c.
width of the confidence interval to remain the same
d.
sample size to increase
38. In developing an interval estimate of the population mean, if the population standard deviation is unknown
a.
it is impossible to develop an interval estimate
b.
a sample proportion can be used
c.
the sample standard deviation and t distribution can be used
d.
None of the other answers are correct.
c
39. A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50
times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2
minutes. Which Excel function would be used to construct a confidence interval estimate?
a.
CONFIDENCE.NORM
b.
NORM.INV
c.
T.INV
d.
INT
a
40. An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random
sample of 200 current owners is taken. The population standard deviation is known. Which Excel function would not be
appropriate to use to construct a confidence interval estimate?
a.
NORM.S.INV
b.
COUNTIF
c.
AVERAGE
d.
STDEV
41. Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate
for a population mean?
a.
standard distribution
b.
z distribution
c.
binomial distribution
d.
t distribution
42. The t distribution should be used whenever
a.
the sample size is less than 30
b.
the sample standard deviation is used to estimate the population standard deviation
c.
the population is not normally distributed
d.
None of the other answers are correct.
43. Whenever using the t distribution in interval estimation, we must assume that the
a.
sample size is less than 30
b.
degrees of freedom equals n − 1
c.
population is approximately normal
d.
finite population correction factor is necessary
44. From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is
selected. For the interval estimation of μ, the proper distribution to use is the
a.
standard normal distribution
b.
z distribution
c.
t distribution with 26 degrees of freedom
d.
t distribution with 24 degrees of freedom
45. From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is
selected to develop an interval estimate for μ. Which of the following statements is true?
a.
The standard normal distribution can be used.
b.
The t distribution with 50 degrees of freedom must be used.
c.
The t distribution with 49 degrees of freedom must be used.
d.
The sample size must be increased in order to develop an interval estimate.
c
46. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the
standard normal distribution
a.
becomes larger
b.
becomes smaller
c.
stays the same
d.
None of the other answers are correct.
47. The t value with a 95% confidence and 24 degrees of freedom is
a.
1.711
b.
2.064
c.
2.492
d.
2.069
48. A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard
deviation of 4. The 95% confidence interval for μ is
Chapter 8 – Interval Estimation
a.
6.000 to 14.000
b.
9.846 to 10.154
c.
8.384 to 11.616
d.
8.462 to 11.538
49. A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all
students at the college are normally distributed with a standard deviation of 1.8 years. The 98% confidence interval for the
average age of all students at this college is
a.
24.301 to 25.699
b.
24.385 to 25.615
c.
23.200 to 26.800
d.
23.236 to 26.764
50. A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of
144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination
score is
a.
70.02 to 81.98
b.
69.82 to 82.18
c.
70.06 to 81.94
d.
69.48 to 82.52
51. A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the
mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?
a.
95% of the sample of employees has a systolic blood pressure between 123 and 139.
b.
If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain
the population mean systolic blood pressure.
c.
95% of the population of employees has a systolic blood pressure between 123 and 139.
d.
If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and
139.
52. To estimate a population mean, the sample size needed to provide a margin of error of 2 or less with a .95 probability
when the population standard deviation equals 11 is
a.
10
b.
11
c.
116
d.
117
53. It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to
estimate the population mean if the desired margin of error is 5 or less is
a.
25
b.
74
c.
189
d.
75
54. We can use the normal distribution to make confidence interval estimates for the population proportion, p, when
a.
np ≥ 5
b.
n(1 − p) ≥ 5
c.
p has a normal distribution
d.
Both np ≥ 5 and n(1 − p) ≥ 5
55. Using an α = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of
significance is decreased, the interval for the population proportion
a.
becomes narrower
b.
becomes wider
c.
does not change
d.
Not enough information is provided to answer this question.
56. In determining the sample size necessary to estimate a population proportion, which of the following information is
not needed?
a.
the maximum margin of error that can be tolerated
b.
the confidence level required
c.
a preliminary estimate of the true population proportion p
d.
the mean of the population
57. For which of the following values of p is the value of p(1 − p) maximized?
a.
p = 0.99
b.
p = 0.90
c.
p = 1.0
d.
p = 0.50
58. A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random
sample of 50 items is taken. Which Excel function would not be appropriate to construct a confidence interval estimate?
Chapter 8 – Interval Estimation
a.
NORM.S.INV
b.
COUNTIF
c.
STDEV
d.
All are appropriate.
c
59. A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000
voters is taken. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be
used to construct a confidence interval estimate?
a.
NORM.S.INV
b.
NORM.INV
c.
T.INV
d.
INT
a
60. The general form of an interval estimate of a population mean or population proportion is the _____ plus and minus
the _____.
a.
population mean, standard error
b.
level of significance, degrees of freedom
c.
point estimate, margin of error
d.
planning value, confidence coefficient
c
61. The degrees of freedom associated with a t distribution are a function of the
a.
area in the upper tail
b.
sample standard deviation
c.
confidence coefficient
d.
sample size
62. The margin of error in an interval estimate of the population mean is a function of all of the following except
a.
level of significance
b.
sample mean
c.
sample size
d.
variability of the population
63. To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures
are recommended when
is unknown except
a.
use the estimated
from a previous study
Chapter 8 – Interval Estimation
b.
use the sample standard deviation from a preliminary sample
c.
use judgment or a best guess
d.
use .5 as a conservative estimate
64. To compute the necessary sample size for an interval estimate of a population proportion, all of the following
procedures are recommended when p is unknown except
a.
use the sample proportion from a previous study
b.
use the sample proportion from a preliminary sample
c.
use 1.0 as an estimate
d.
use judgment or a best guess
65. When σ is known, the margin of error in a confidence interval estimate
a.
varies from sample to sample of the same size
b.
is the same for all samples of the same size
c.
increases as the sample size increases
d.
is independent of sample size
66. If we have a finite population such that n/N > .05, the desired margin of error can be obtained using
a.
a smaller sample size than the one needed if the population were infinite
b.
a larger sample size than the one needed if the population were infinite
c.
the same sample size as the one needed if the population were infinite
d.
a sample size of 30 or more
Subjective Short Answer
67. In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage
determined.
a.
Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of
the mean.
b.
With a 0.95 probability, determine the margin of error.
c.
If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the
population mean?
a.
25
b.
49
c.
1951 to 2049
68. A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is
known that the standard deviation of the population is $40.00.