Confidence Interval Estimation 8-1
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATION
1. True or False: A point estimate consists of a single sample statistic that is used to estimate the
true population parameter.
2. True or False: The sample mean is a point estimate of the population mean.
3. The head librarian at the Library of Congress has asked her assistant for an interval estimate
of the mean number of books checked out each day. The assistant provides the following
interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point
estimate of the number of books checked out each day at the Library of Congress?
a) 740
b) 830
c) 920
d) 1,660
4. Private colleges and universities rely on money contributed by individuals and corporations
for their operating expenses. Much of this money is put into a fund called an endowment, and
the college spends only the interest earned by the fund. A recent survey of 8 private colleges
in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0,
235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for
the mean endowment of all private colleges in the United States?
a) $1,447.8
b) $180.975
c) $143.042
d) $8
8-2 Confidence Interval Estimation
5. True or False: A population parameter is used to estimate a confidence interval.
6. True or False: For a given data set, the confidence interval will be wider for 95% confidence
than for 90% confidence.
7. True or False: Holding the sample size fixed, increasing the level of confidence in a
confidence interval will necessarily lead to a wider confidence interval.
8. True or False: Holding the level of confidence fixed, increasing the sample size will lead to a
wider confidence interval.
9. True or False: Holding the width of a confidence interval fixed, increasing the level of
confidence can be achieved with a lower sample size.
Confidence Interval Estimation 8-3
10. Suppose a 95% confidence interval for
μ
turns out to be (1,000, 2,100). To make more
useful inferences from the data, it is desired to reduce the width of the confidence interval.
Which of the following will result in a reduced interval width?
a) Increase the sample size.
b) Increase the confidence level.
c) Increase the population mean.
d) Increase the sample mean.
11. Suppose a 95% confidence interval for
μ
has been constructed. If it is decided to take a
larger sample and to decrease the confidence level of the interval, then the resulting interval
width would . (Assume that the sample statistics gathered would not
change very much for the new sample.)
a) be larger than the current interval width
b) be narrower than the current interval width
c) be the same as the current interval width
d) be unknown until actual sample sizes and reliability levels were determined
12. In the construction of confidence intervals, if all other quantities are unchanged, an increase
in the sample size will lead to a interval.
a) narrower
b) wider
c) less significant
d) biased
13. True or False: Other things being equal, as the confidence level for a confidence interval
increases, the width of the interval increases.
8-4 Confidence Interval Estimation
14. True or False: The confidence interval obtained will always correctly estimate the population
parameter.
15. True or False: Other things being equal, the confidence interval for the mean will be wider for
95% confidence than for 90% confidence.
16. True or False: The difference between the upper limit of a confidence interval and the point
estimate used in constructing the confidence interval is called the sampling error.
17. True or False: The difference between the lower limit of a confidence interval and the point
estimate used in constructing the confidence interval is called the sampling error.
18. True or False: Sampling error equals half the width of a confidence interval.
19. True or False: The width of a confidence interval equals twice the sampling error.
20. True or False: The sampling error can either be positive or negative.
21. True or False: The difference between the sample mean and the population mean is called the
sampling error.
22. True or False: The difference between the sample proportion and the population proportion is
called the sampling error.
23. True or False: The difference between the sample size and the population size is called the
sampling error.
24. True or False: The confidence interval estimate of the population mean is constructed around
the sample mean.
8-6 Confidence Interval Estimation
25. A 99% confidence interval estimate can be interpreted to mean that
a) if all possible samples of size n are taken and confidence interval estimates are
developed, 99% of them would include the true population mean somewhere
within their interval.
b) we have 99% confidence that we have selected a sample whose interval does
include the population mean.
c) Both of the above.
d) None of the above.
26. An economist is interested in studying the incomes of consumers in a particular country. The
population standard deviation is known to be $1,000. A random sample of 50 individuals
resulted in a mean income of $15,000. What is the upper end point in a 99% confidence
interval for the average income?
a) $15,052
b) $15,141
c) $15,330
d) $15,364
27. An economist is interested in studying the incomes of consumers in a particular country. The
population standard deviation is known to be $1,000. A random sample of 50 individuals
resulted in a mean income of $15,000. What is the width of the 90% confidence interval?
a) $232.60
b) $364.30
c) $465.23
d) $728.60
28. True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a
sample of 10 data points, a 90% confidence interval will have a width of 2.36.
Confidence Interval Estimation 8-7
29. True or False: A sample size of 5 provides a sample mean of 9.6. If the population variance is
known to be 5 and the population distribution is assumed to be normal, the lower limit for a
90% confidence interval is 7.96.
30. The t distribution approaches the standardized normal distribution when the number of
degrees of freedom increases.
31. True or False: The t distribution is used to develop a confidence interval estimate of the
population mean when the population standard deviation is unknown.
32. True or False: For a t distribution with 12 degrees of freedom, the area between – 2.6810 and
2.1788 is 0.980.
33. If you were constructing a 99% confidence interval of the population mean based on a sample
of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be
a) 2.7969
b) 2.7874
c) 2.4922
d) 2.4851
8-8 Confidence Interval Estimation
34. Which of the following is not true about the Student’s t distribution?
a) It has more area in the tails and less in the center than does the normal
distribution.
b) It is used to construct confidence intervals for the population mean when the
population standard deviation is known.
c) It is bell shaped and symmetrical.
d) As the number of degrees of freedom increases, the t distribution approaches the
normal distribution.
35. True or False: The t distribution is used to construct confidence intervals for the population
mean when the population standard deviation is unknown.
36. The t distribution
a) assumes the population is normally distributed.
b) approaches the normal distribution as the sample size increases.
c) has more area in the tails than does the normal distribution.
d) All of the above.
37. It is desired to estimate the mean total compensation of CEOs in the Service industry. Data
were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be
($2,181,260, $5,836,180). Which of the following interpretations is correct?
a) 95% of the sampled total compensation values fell between $2,181,260 and
$5,836,180.
b) We are 95% confident that the mean of the sampled CEOs falls in the interval
$2,181,260 to $5,836,180.
c) In the population of Service industry CEOs, 95% of them will have total
compensations that fall in the interval $2,181,260 to $5,836,180.
d) We are 95% confident that the mean total compensation of all CEOs in the
Service industry falls in the interval $2,181,260 to $5,836,180.
Confidence Interval Estimation 8-9
38. It is desired to estimate the mean total compensation of CEOs in the Service industry. Data
were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be
($2,181,260, $5,836,180). Based on the interval above, do you believe the mean total
compensation of CEOs in the Service industry is more than $3,000,000?
a) Yes, and I am 95% confident of it.
b) Yes, and I am 78% confident of it.
c) I am 95% confident that the mean compensation is $3,000,000.
d) I cannot conclude that the mean exceeds $3,000,000 at the 95% confidence level.
39. Suppose a 95% confidence interval for
μ
turns out to be (1,000, 2,100). Give a definition of
what it means to be “95% confident” as an inference.
a) In repeated sampling, the population parameter would fall in the given interval
95% of the time.
b) In repeated sampling, 95% of the intervals constructed would contain the
population mean.
c) 95% of the observations in the entire population fall in the given interval.
d) 95% of the observations in the sample fall in the given interval.
40. A major department store chain is interested in estimating the mean amount its credit card
customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card
accounts were randomly sampled and analyzed with the following results: X =$50.50 and
20S=. Assuming the distribution of the amount spent on their first visit is normal, what is
the shape of the sampling distribution of the sample mean that will be used to create the
desired confidence interval for
μ
?
a) Approximately normal with a mean of $50.50
b) A standard normal distribution
c) A t distribution with 15 degrees of freedom
d) A t distribution with 14 degrees of freedom
8-10 Confidence Interval Estimation
41. A major department store chain is interested in estimating the mean amount its credit card
customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card
accounts were randomly sampled and analyzed with the following results: $50.50X= and
20S=. Construct a 95% confidence interval for the mean amount its credit card customers
spent on their first visit to the chain’s new store in the mall assuming that the amount spent
follows a normal distribution.
a) $50.50 ± $9.09
b) $50.50 ± $10.12
c) $50.50 ± $11.00
d) $50.50 ± $11.08
42. Private colleges and universities rely on money contributed by individuals and corporations
for their operating expenses. Much of this money is put into a fund called an endowment, and
the college spends only the interest earned by the fund. A recent survey of 8 private colleges
in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0,
235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield X =180.975 and
143.042S=. Calculate a 95% confidence interval for the mean endowment of all the private
colleges in the United States assuming a normal distribution for the endowments.
a) $180.975±$94.066
b) $180.975±$99.123
c) $180.975±$116.621
d) $180.975±$119.586
43. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-
hour period. The director randomly selects 64 different 24-hour periods and determines the
number of admissions for each. For this sample, 396X= and S = 100. Which of the
following assumptions is necessary in order for a confidence interval to be valid?
a) The population sampled from has an approximate normal distribution.
b) The population sampled from has an approximate t distribution.
c) The mean of the sample equals the mean of the population.
d) None of these assumptions are necessary.
Confidence Interval Estimation 8-11
44. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-
hour period. The director randomly selects 64 different 24-hour periods and determines the
number of admissions for each. For this sample, 396X= and S = 100. Estimate the mean
number of admissions per 24-hour period with a 95% confidence interval.
45. True or False: In estimating the population mean with the population standard deviation
unknown, if the sample size is 12, there will be 6 degrees of freedom.
46. True or False: A race car driver tested his car for time from 0 to 60 mph, and for 20 tests
obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95%
confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.
47. True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a
sample of 10 data points, a 90% confidence interval will have a width of 2.36.
48. True or False: A random sample of 50 provides a sample mean of 31 with a standard
deviation of S = 14. The upper bound of a 90% confidence interval estimate of the population
mean is 34.32.
8-12 Confidence Interval Estimation
49. True or False: In forming a 90% confidence interval for a population mean from a sample
size of 22, the number of degrees of freedom from the t distribution equals 22.
50. True or False: The t distribution allows the calculation of confidence intervals for means
when the actual standard deviation is not known.
51. True or False: The t distribution allows the calculation of confidence intervals for means for
small samples when the population variance is not known, regardless of the shape of the
distribution in the population.
52. A university dean is interested in determining the proportion of students who receive some
sort of financial aid. Rather than examine the records for all students, the dean randomly
selects 200 students and finds that 118 of them are receiving financial aid. Use a 90%
confidence interval to estimate the true proportion of students who receive financial aid.
Confidence Interval Estimation 8-13
53. A university dean is interested in determining the proportion of students who receive some
sort of financial aid. Rather than examine the records for all students, the dean randomly
selects 200 students and finds that 118 of them are receiving financial aid. The 95%
confidence interval for
π
is 0.59 ± 0.07. Interpret this interval.
a) We are 95% confident that the true proportion of all students receiving financial
aid is between 0.52 and 0.66.
b) 95% of the students get between 52% and 66% of their tuition paid for by
financial aid.
c) We are 95% confident that between 52% and 66% of the sampled students
receive some sort of financial aid.
d) We are 95% confident that 59% of the students are on some sort of financial aid.
54. The county clerk wants to estimate the proportion of voters who will need special election
facilities. The clerk wants to construct a 95% confidence interval for the population
proportion which extends at most 0.07 to either side of the sample proportion. How large a
sample must be taken to assure these conditions are met?
55. The county clerk wants to estimate the proportion of voters who will need special election
facilities. Suppose a sample of 400 voters was taken. If 150 need special election facilities,
calculate an 90% confidence interval for the population proportion.
56. A quality control engineer is interested in estimating the proportion of defective items coming
off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval
for the proportion of defectives from this production line would go from __________ to
__________.
8-14 Confidence Interval Estimation
57. A prison official wants to estimate the proportion of cases of recidivism. Examining the
records of 250 convicts, the official determines that there are 65 cases of recidivism. A
confidence interval will be obtained for the proportion of cases of recidivism. Part of this
calculation includes the estimated standard error of the sample proportion. For this sample,
the estimated standard error is __________.
58. A prison official wants to estimate the proportion of cases of recidivism. Examining the
records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99%
confidence interval for the proportion of cases of recidivism would go from __________ to
__________.
59. True or False: A sample of 100 fuses from a very large shipment is found to have 10 that are
defective. The 95% confidence interval would indicate that, for this shipment, the proportion
of defective fuses is between 0 and 0.28.
60. True or False: The confidence interval estimate of the population proportion is constructed
around the sample proportion.
61. True or False: The t distribution is used to develop a confidence interval estimate of the
population proportion when the population standard deviation is unknown.
Confidence Interval Estimation 8-15
62. True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion regardless of whether the population standard deviation
is known.
63. True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion when the sample size is sufficiently large.
64. True or False: The width of a confidence interval estimate for a proportion will be
a) narrower for 99% confidence than for 95% confidence.
b) wider for a sample size of 100 than for a sample size of 50.
c) narrower for 90% confidence than for 95% confidence.
d) narrower when the sample proportion is 0.50 than when the sample proportion is
0.20.
65. When determining the sample size for a proportion for a given level of confidence and
sampling error, the closer to 0.50 that
π
is estimated to be, the sample size required
__________.
a) is smaller
b) is larger
c) is not affected
d) can be smaller, larger or unaffected
8-16 Confidence Interval Estimation
66. A confidence interval was used to estimate the proportion of statistics students who are
females. A random sample of 72 statistics students generated the following 90% confidence
interval: (0.438, 0.642). Based on the interval above, is the population proportion of females
equal to 0.60?
a) No, and we are 90% sure of it.
b) No. The proportion is 54.17%.
c) Maybe. 0.60 is a believable value of the population proportion based on the
information above.
d) Yes, and we are 90% sure of it.
67. When determining the sample size necessary for estimating the true population mean, which
factor is not considered when sampling with replacement?
a) The population size.
b) The population standard deviation.
c) The level of confidence desired in the estimate.
d) The allowable or tolerable sampling error.
68. The head librarian at the Library of Congress has asked her assistant for an interval estimate
of the mean number of books checked out each day. The assistant provides the following
interval estimate: from 740 to 920 books per day. If the head librarian knows that the
population standard deviation is 150 books checked out per day, approximately how large a
sample did her assistant use to determine the interval estimate?
a) 2
b) 3
c) 12
d) It cannot be determined from the information given.
Confidence Interval Estimation 8-17
69. The head librarian at the Library of Congress has asked her assistant for an interval estimate
of the mean number of books checked out each day. The assistant provides the following
interval estimate: from 740 to 920 books per day. If the head librarian knows that the
population standard deviation is 150 books checked out per day, and she asked her assistant
for a 95% confidence interval, approximately how large a sample did her assistant use to
determine the interval estimate?
a) 125
b) 13
c) 11
d) 4
70. The head librarian at the Library of Congress has asked her assistant for an interval estimate
of the mean number of books checked out each day. The assistant provides the following
interval estimate: from 740 to 920 books per day. If the head librarian knows that the
population standard deviation is 150 books checked out per day, and she asked her assistant
to use 25 days of data to construct the interval estimate, what confidence level can she attach
to the interval estimate?
a) 99.7%
b) 99.0%
c) 98.0%
d) 95.4%
71. An economist is interested in studying the incomes of consumers in a particular country. The
population standard deviation is known to be $1,000. A random sample of 50 individuals
resulted in a mean income of $15,000. What total sample size would the economist need to
use for a 95% confidence interval if the width of the interval should not be more than $100?
a) n = 1537
b) n = 385
c) n = 40
d) n = 20
8-18 Confidence Interval Estimation
72. As an aid to the establishment of personnel requirements, the director of a hospital wishes to
estimate the mean number of people who are admitted to the emergency room during a 24-
hour period. The director randomly selects 64 different 24-hour periods and determines the
number of admissions for each. For this sample, 396X= and S = 100. Using the sample
standard deviation as an estimate for the population standard deviation, what size sample
should the director choose if she wishes to estimate the mean number of admissions per 24-
hour period to within 1 admission with 99% reliability,?
73. Suppose a department store wants to estimate the mean age of the customers of its
contemporary apparel department, correct to within 2 years, with level of confidence equal to
95%. Management believes that the standard deviation is 8 years. The sample size they
should take is ________.
74. A university dean is interested in determining the proportion of students who receive some
sort of financial aid. Rather than examine the records for all students, the dean randomly
selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted
to estimate the proportion of all students receiving financial aid to within 3% with 99%
reliability, how many students would need to be sampled?
a) n = 1,844
b) n = 1,784
c) n = 1,503
d) n = 1,435
Confidence Interval Estimation 8-19
75. A confidence interval was used to estimate the proportion of statistics students who are
female. A random sample of 72 statistics students generated the following 90% confidence
interval: (0.438, 0.642). Using the information above, what total size sample would be
necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?
a) 105
b) 150
c) 420
d) 597
76. A university system enrolling hundreds of thousands of students is considering a change in
the way students pay for their education. Currently, the students pay $400 per credit hour.
The university system administrators are contemplating charging each student a set fee of
$7,000 per quarter, regardless of how many credit hours each takes. To see if this proposal
would be economically feasible, the administrators would like to know how many credit
hours, on the average, each student takes per quarter. A random sample of 250 students yields
a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per
quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95%
reliability and assumed that the sample standard deviation provided a good estimate for the
population standard deviation. How large a total sample would they need to take?
SCENARIO 8-1
The managers of a company are worried about the morale of their employees. In order to
determine if a problem in this area exists, they decide to evaluate the attitudes of their
employees with a standardized test. They select the Fortunato test of job satisfaction,
which has a known standard deviation of 24 points.
77. Referring to Scenario 8-1, they should sample ________ employees if they want to estimate
the mean score of the employees within 5 points with 90% confidence.
8-20 Confidence Interval Estimation
78. Referring to Scenario 8-1, due to financial limitations, the managers decide to take a sample
of 45 employees. This yields a mean score of 88.0 points. A 90% confidence interval would
go from ________ to ________.
79. True or False: Referring to Scenario 8-1, this confidence interval is only valid if the scores on
the Fortunato test are normally distributed.
SCENARIO 8-2
A quality control engineer is interested in the mean length of sheet insulation being cut
automatically by machine. The desired mean length of the insulation is 12 feet. It is
known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut
sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99%
confidence interval for the mean length cut by machine.
80. Referring to Scenario 8-2, the critical value to use in obtaining the confidence interval is
________.
81. Referring to Scenario 8-2, the confidence interval goes from ________ to ________.
Confidence Interval Estimation 8-21
82. True or False: Referring to Scenario 8-2, the confidence interval indicates that the machine is
not working properly.
83. True or False: Referring to Scenario 8-2, the confidence interval is valid only if the lengths
cut are normally distributed.
84. Referring to Scenario 8-2, suppose the engineer had decided to estimate the mean length to
within 0.03 with 99% confidence. Then the sample size would be ________.
SCENARIO 8-3
To become an actuary, it is necessary to pass a series of 10 exams, including the most
important one, an exam in probability and statistics. An insurance company wants to
estimate the mean score on this exam for actuarial students who have enrolled in a special
study program. They take a sample of 8 actuarial students in this program and determine
that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90%
confidence interval for the mean score for actuarial students in the special study program.
85. Referring to Scenario 8-3, the mean of the sample is __________, while the standard
deviation of the sample is __________.
8-22 Confidence Interval Estimation
86. Referring to Scenario 8-3, the confidence interval will be based on __________ degrees of
freedom.
87. Referring to Scenario 8-3, the critical value used in constructing a 90% confidence interval is
__________.
88. Referring to Scenario 8-3, a 90% confidence interval for the mean score of actuarial students
in the special program is from __________ to __________.
89. True or False: Referring to Scenario 8-3, for the confidence interval to be valid, it is
necessary that test scores of students in the special study program on the actuarial exam be
normally distributed.
90. True or False: Referring to Scenario 8-3, it is possible that the confidence interval obtained
will not contain the mean score for all actuarial students in the special study program.
91. True or False: Referring to Scenario 8-3, if we use the same sample information to obtain a
95% confidence interval, the resulting interval would be narrower than the one obtained here
with 90% confidence.
Confidence Interval Estimation 8-23
SCENARIO 8-4
The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64,
11.84, 12.13, 11.99, and 11.77.
92. Referring to Scenario 8-4, a confidence interval for this sample would be based on the t
distribution with __________ degrees of freedom.
93. Referring to Scenario 8-4, the critical value for a 99% confidence interval for this sample is
__________.
94. Referring to Scenario 8-4, a 99% confidence interval for the mean voltage of the power packs
is from __________ to __________.
95. True or False: Referring to Scenario 8-4, a 95% confidence interval for the mean voltage of
the power pack is wider than a 99% confidence interval.
96. True or False: Referring to Scenario 8-4, a 99% confidence interval will contain 99% of the
voltages for all such power packs.
8-24 Confidence Interval Estimation
97. True or False: Referring to Scenario 8-4, a confidence interval estimate of the population
mean would only be valid if the distribution of voltages is normal.
98. True or False: Referring to Scenario 8-4, a 90% confidence interval calculated from the same
data would be narrower than a 99% confidence interval.
99. True or False: Referring to Scenario 8-4, it is possible that the 99% confidence interval
calculated from the data will not contain the mean voltage for the sample.
100. True or False: Referring to Scenario 8-4, it is possible that the 99% confidence interval
calculated from the data will not contain the mean voltage for the entire population.
SCENARIO 8-5
A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46,
52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval
resulted in an interval from 47.19 to 52.61.
101. True or False: Referring to Scenario 8-5, 95% of the time, the sample mean salary offer to
management majors will fall between 47.19 and 52.61.
Confidence Interval Estimation 8-25
102. True or False: Referring to Scenario 8-5, 95% of the salary offers are between 47.19 and
52.61.
103. True or False: Referring to Scenario 8-5, it is possible that the mean of the population is
between 47.19 and 52.61.
104. True or False: Referring to Scenario 8-5, it is possible that the mean of the population is not
between 47.19 and 52.61.
105. True or False: Referring to Scenario 8-5, 95% of the sample means will fall between 47.19
and 52.61.
106. True or False: Referring to Scenario 8-5, 95% of all confidence intervals constructed
similarly to this one with a sample size of 10 will contain the mean of the population.
107. True or False: Referring to Scenario 8-5, a 99% confidence interval for the mean of the
population from the same sample would be wider than 47.19 to 52.61.
8-26 Confidence Interval Estimation
108. True or False: Referring to Scenario 8-5, the confidence interval obtained is valid only if
the distribution of the population of salary offers is normal.
SCENARIO 8-6
After an extensive advertising campaign, the manager of a company wants to estimate the
proportion of potential customers that recognize a new product. She samples 120
potential consumers and finds that 54 recognize this product. She uses this sample
information to obtain a 95% confidence interval that goes from 0.36 to 0.54.
109. True or False: Referring to Scenario 8-6, the parameter of interest to the manager is the
proportion of potential customers in this sample that recognize the new product.
110. True or False: Referring to Scenario 8-6, the parameter of interest is 54/120 = 0.45.
111. True or False: Referring to Scenario 8-6, this interval requires the use of the t distribution to
obtain the confidence coefficient.
112. True or False: Referring to Scenario 8-6, this interval requires the assumption that the
distribution of the number of people recognizing the product has a normal distribution.
Confidence Interval Estimation 8-27
113. True or False: Referring to Scenario 8-6, 95% of the time, the proportion of people that
recognize the product will fall between 0.36 and 0.54.
114. True or False: Referring to Scenario 8-6, 95% of the time, the sample proportion of people
that recognize the product will fall between 0.36 and 0.54.
115. True or False: Referring to Scenario 8-6, 95% of the people will recognize the product
between 36% and 54% of the time.
116. True or False: Referring to Scenario 8-6, it is possible that the true proportion of people
that recognize the product is between 0.36 and 0.54.
117. True or False: Referring to Scenario 8-6, it is possible that the true proportion of people
that recognize the product is not between 0.36 and 0.54.
8-28 Confidence Interval Estimation
118. The head of a computer science department is interested in estimating the proportion of
students entering the department who will choose the new computer engineering option.
Suppose there is no information about the proportion of students who might choose the
option. What size sample should the department head take if she wants to be 95% confident
that the estimate is within 0.10 of the true proportion?
119. The head of a computer science department is interested in estimating the proportion of
students entering the department who will choose the new computer engineering option. A
preliminary sample indicates that the proportion will be around 0.25. Therefore, what size
sample should the department head take if she wants to be 95% confident that the estimate is
within 0.10 of the true proportion?
SCENARIO 8-7
A hotel chain wants to estimate the mean number of rooms rented daily in a given month.
The population of rooms rented daily is assumed to be normally distributed for each month
with a standard deviation of 240 rooms. During February, a sample of 25 days has a sample
mean of 370 rooms.
120. True or False: Referring to Scenario 8-7, the parameter of interest is the mean number of
rooms rented daily in a given month.
121. True or False: Referring to Scenario 8-7, the parameter of interest is the proportion of the
rooms rented daily in a given month.
Confidence Interval Estimation 8-29
122. Referring to Scenario 8-7, the critical value for a 99% confidence interval for this sample is
__________.
123. Referring to Scenario 8-7, a 99% confidence interval for the mean number of rooms rented
daily in a given month is from __________ to __________.
124. Referring to Scenario 8-7, the sampling error of a 99% confidence interval for the mean
number of rooms rented daily in a given month is __________.
125. True or False: Referring to Scenario 8-7, a 95% confidence interval for the mean number
of rooms rented daily in a given month is narrower than a 99% confidence interval.
126. True or False: Referring to Scenario 8-7, a 99% confidence interval will contain 99% of the
sample mean number of rooms rented daily in a given month.
127. True or False: Referring to Scenario 8-7, a 90% confidence interval calculated from the
same data would be narrower than a 99% confidence interval.
8-30 Confidence Interval Estimation
128. True or False: Referring to Scenario 8-7, it is possible that the 99% confidence interval
calculated from the data will not contain the sample mean number of rooms rented daily in a
given month.
129. True or False: Referring to Scenario 8-7, it is possible that the 99% confidence interval
calculated from the data will not contain the population mean number of rooms rented daily
in a given month.
130. True or False: Referring to Scenario 8-7, we are 99% confident that between 246.36% and
493.64% of the rooms will be rented daily in a given month.
131. True or False: Referring to Scenario 8-7, we are 99% confident that the average number of
rooms rented daily in a given month is somewhere between 246.36 and 493.64.
SCENARIO 8-8
The president of a university would like to estimate the proportion of the student population
that owns a personal computer. In a sample of 500 students, 417 own a personal computer.
132. True or False: Referring to Scenario 8-8, the parameter of interest is the mean number of
students in the population who own a personal computer.
Confidence Interval Estimation 8-31
133. True or False: Referring to Scenario 8-8, the parameter of interest is the proportion of the
student population who own a personal computer.
134. Referring to Scenario 8-8, the critical value for a 99% confidence interval for this sample is
__________.
135. Referring to Scenario 8-8, a 99% confidence interval for the proportion of the student
population who own a personal computer is from __________ to __________.
136. Referring to Scenario 8-8, the sampling error of a 99% confidence interval for the
proportion of the student population who own a personal computer is __________.
137. True or False: Referring to Scenario 8-8, a 95% confidence interval for the proportion of
the student population who own a personal computer is narrower than a 99% confidence
interval.
138. True or False: Referring to Scenario 8-8, a 99% confidence interval will contain 99% of the
student population who own a personal computer.
8-32 Confidence Interval Estimation
139. True or False: Referring to Scenario 8-8, a confidence interval estimate of the population
proportion would only be valid if the distribution of the number of students who own a
personal computer is normal.
140. True or False: Referring to Scenario 8-8, a 90% confidence interval calculated from the
same data would be narrower than a 99% confidence interval.
141. True or False: Referring to Scenario 8-8, it is possible that the 99% confidence interval
calculated from the data will not contain the sample proportion of students who own a
personal computer.
142. True or False: Referring to Scenario 8-8, it is possible that the 99% confidence interval
calculated from the data will not contain the proportion of the student population who own a
personal computer.
143. True or False: Referring to Scenario 8-8, we are 99% confident that the mean numbers of
student population who own a personal computer is between 0.7911 and 0.8769.
Confidence Interval Estimation 8-33
144. True or False: Referring to Scenario 8-8, we are 99% confident that between 79.11% and
87.69% of the student population own a personal computer.
SCENARIO 8-9
A university wanted to find out the percentage of students who felt comfortable reporting
cheating by their fellow students. A surveyed of 2,800 students was conducted and the
students were asked if they felt comfortable reporting cheating by their fellow students. The
results were 1,344 answered “Yes” and 1,456 answered “no”.
145. True or False: Referring to Scenario 8-9, the parameter of interest is the total number of
students in the population who feel comfortable reporting cheating by their fellow students.
146. True or False: Referring to Scenario 8-9, the parameter of interest is the proportion of the
student population who feel comfortable reporting cheating by their fellow students.
147. Referring to Scenario 8-9, the critical value for a 99% confidence interval for this sample is
__________.
148. Referring to Scenario 8-9, a 99% confidence interval for the proportion of the student
population who feel comfortable reporting cheating by their fellow students is from
__________ to __________.
8-34 Confidence Interval Estimation
149. Referring to Scenario 8-9, the sampling error of a 99% confidence interval for the
proportion of student population who feel comfortable reporting cheating by their fellow
students is __________.
150. True or False: Referring to Scenario 8-9, a 95% confidence interval for the proportion of
the student population who feel comfortable reporting cheating by their fellow students is
narrower than a 99% confidence interval.
151. True or False: Referring to Scenario 8-9, a 99% confidence interval will contain 99% of the
student population who feel comfortable reporting cheating by their fellow students.
152. True or False: Referring to Scenario 8-9, a confidence interval estimate of the population
proportion would only be valid if the distribution of the number of students who feel
comfortable reporting cheating by their fellow students is normal.
153. True or False: Referring to Scenario 8-9, a 90% confidence interval calculated from the
same data would be narrower than a 99% confidence interval.
Confidence Interval Estimation 8-35
154. True or False: Referring to Scenario 8-9, it is possible that the 99% confidence interval
calculated from the data will not contain the sample proportion of students who feel
comfortable reporting cheating by their fellow students.
155. True or False: Referring to Scenario 8-9, it is possible that the 99% confidence interval
calculated from the data will not contain the proportion of the student population who feel
comfortable reporting cheating by their fellow students.
156. True or False: Referring to Scenario 8-9, we are 99% confident that the total number of the
student population who feel comfortable reporting cheating by their fellow students is
between 0.4557 and 0.5043.
157. True or False: Referring to Scenario 8-9, we are 99% confident that between 45.57% and
50.43% of the student population feel comfortable reporting cheating by their fellow students.
8-36 Confidence Interval Estimation
SCENARIO 8-10
A sales and marketing management magazine conducted a survey on salespeople cheating on
their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the
managers have caught salespeople cheating on an expense report, 50% have caught
salespeople working a second job on company time, 22% have caught salespeople listing a
“strip bar” as a restaurant on an expense report, and 19% have caught salespeople giving a
kickback to a customer.
158. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population
proportion of managers who have caught salespeople cheating on an expense report.
159. Referring to Scenario 8-10, the critical value for a 95% confidence interval estimate of the
population proportion of managers who have caught salespeople cheating on an expense
report is __________.
160. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the
population proportion of managers who have caught salespeople cheating on an expense
report is __________.
161. True or False: Referring to Scenario 8-10, a 95% confidence interval will contain 95% of
the population proportion of managers who have caught salespeople cheating on an expense
report.
Confidence Interval Estimation 8-37
162. True or False: Referring to Scenario 8-10, it is possible that the 95% confidence interval
calculated from the data will not contain the sample proportion of managers who have caught
salespeople cheating on an expense report.
163. True or False: Referring to Scenario 8-10, it is possible that the 95% confidence interval
calculated from the data will not contain the population proportion of managers who have
caught salespeople cheating on an expense report.
164. True or False: Referring to Scenario 8-10, we are 95% confident that the population mean
number of managers who have caught salespeople cheating on an expense report is between
0.5116 to 0.6484.
165. True or False: Referring to Scenario 8-10, we are 95% confident that between 51.16% and
64.84% of managers in the population have caught salespeople cheating on an expense
report.
166. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population
proportion of managers who have caught salespeople working a second job on company time.
8-38 Confidence Interval Estimation
167. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the
population proportion of managers who have caught salespeople working a second job on
company time is __________.
168. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population
proportion of managers who have caught salespeople listing a “strip bar” as a restaurant on an
expense report.
169. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the
population proportion of managers who have caught salespeople listing a “strip bar” as a
restaurant on an expense report is __________.
170. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population
proportion of managers who have caught salespeople giving a kickback to a customer.
171. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the
population proportion of managers who have caught salespeople giving a kickback to a
customer is __________.
Confidence Interval Estimation 8-39
172. Referring to Scenario 8-10, determine the sample size needed to estimate the proportion of
managers who have caught salespeople working a second job on company time to within
±0.02 with 95% confidence.
SCENARIO 8-11
A poll was conducted by the marketing department of a video game company to determine
the popularity of a new game that was targeted to be launched in three months. Telephone
interviews with 1,500 young adults were conducted which revealed that 49% said they would
purchase the new game. The margin of error was ±3 percentage points.
173. True or False: Referring to Scenario 8-11, the report contains all the essential components
for an ethical reporting of poll results.
174. True or False: Referring to Scenario 8-11, the size of the population is 1,500.
175. Referring to Scenario 8-11, 1,500 is the size of the
a) population
b) sample
c) frame
d) proportion
8-40 Confidence Interval Estimation
176. True or False: Referring to Scenario 8-11, you are 99% confidence that the percentage of
the targeted young adults who will purchase the new game is somewhere between 46% and
52%.
177. True or False: Referring to Scenario 8-11, the standard error is 3%.
178. True or False: Referring to Scenario 8-11, the sampling error is 3%.
179. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence
interval estimate of the percentage of the targeted young adults who will purchase the new
game by allowing the same level of margin of error?
180. Referring to Scenario 8-11, what is the needed sample size to obtain a 90% confidence
interval estimate of the percentage of the targeted young adults who will purchase the new
game by allowing the same level of margin of error?
181. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence
interval in estimating the percentage of the targeted young adults who will purchase the new
game to within ±5%?
Confidence Interval Estimation 8-41
182. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence
interval in estimating the percentage of the targeted young adults who will purchase the new
game to within ±5% if you do not have the information on the 49% in the interviews who
said that they would purchase the new game?
183. Referring to Scenario 8-11, what is the needed sample size to obtain a 99% confidence
interval in estimating the percentage of the targeted young adults who will purchase the new
game to within ±5% if you do not have the information on the 49% in the interviews who
said that they would purchase the new game?