53. If we have some idea about the value of sample proportion , we use that value in determining the
sample size needed to estimate the population proportion p.
54. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is
between 0 and 0.28.
55. A professor of statistics refutes the claim that the proportion of Republican voters in Michigan is at
most 44%. To test the claim, the hypotheses: H0: p = 0.44, H1: p 0.44, should be used.
56. In selecting the sample size to estimate the population proportion p, if we have no knowledge of even
the approximate values of the sample proportion , we:
a.
take another sample and estimate .
b.
take two more samples and find the average of their .
c.
let = 0.50.
d.
let = 0.95.
57. Under what condition(s) does the test statistic for p have an approximate normal distribution?
a.
When np > 5.
b.
When np and np(1 − p) are both > 5.
c.
When n > 30.
d.
When np and n(1 − p) are both > 5.
58. The use of the standard normal distribution for constructing confidence interval estimate for the
population proportion p requires:
a.
n and n(1 − ) both greater than 5.
b.
np and n(1 − p) both greater than 5.
c.
n(1 + ) and n(1 − ) both greater than 5.
d.
sample size greater than 5.
59. After calculating the sample size needed to estimate a population proportion to within 0.04, your
statistics professor told you the maximum allowable error must be reduced to just .01. If the original
calculation led to a sample size of 800, the sample size will now have to be:
a.
800
b.
3,200
c.
6,400
d.
12,800
60. Assuming that all necessary conditions are met, what needs to be changed in the formula
so that we can use it to construct a (1 −
) confidence interval estimate for the
population proportion p?
a.
should be replaced by p.
b.
t
should be replaced by z
.
c.
t
should be replaced by t
/ 2.
d.
t
should be replaced by z / 2.
61. The width of a confidence interval estimate for a proportion will be:
a.
narrower for 90% confidence than for 95% confidence.
b.
wider for a sample size of 100 than for a sample size of 50.
c.
narrower for 99% confidence than for 95% confidence.
d.
narrower when the sample proportion if 0.50 than when the sample proportion is 0.20.
62. When determining the sample size needed for a proportion for a given level of confidence and
sampling error, the closer to 0.50 that p is estimated to be:
a.
the smaller the sample size required.
b.
the larger the sample size required.
c.
the sample size is not affected.
d.
the effect cannot be determined from the information given.
63. Which of the following would be an appropriate null hypothesis?
a.
The population proportion is equal to 0.60.
b.
The sample proportion is equal to 0.60.
c.
The population proportion is not equal to 0.60.
d.
All of these choices are true.
64. Which of the following would be an appropriate alternative hypothesis?
a.
The population proportion is less than 0.65.
b.
The sample proportion is less than 0.65.
c.
The population proportion is equal to 0.65.
d.
The sample proportion is equal to 0.65.
65. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test
this claim against the alternative that the actual proportion of doctors who recommend aspirin is less
than 0.90, a random sample of 100 doctors’ results in 83 who indicate that they recommend aspirin.
The value of the test statistic in this problem is approximately equal to:
a.
−1.67
b.
−2.33
c.
−1.86
d.
−0.14
66. From a sample of 400 items, 14 are found to be defective. The point estimate of the population
proportion defective will be:
a.
0.035
b.
0.05
c.
14
d.
28.57
67. Estimating or testing for p is used in situations when the data are ____________________.
68. The test statistic for p is approximately normal when ____________________ and
____________________ are both greater than 5.
69. The test statistic for p is approximately normal when np and n(1 − p) are both
____________________.
70. To test to see if the majority of the population exhibits a certain characteristic of interest, the
alternative hypothesis of the test is H1: p ____________________.
71. When a population is small, it is necessary to include the ____________________ factor in our
hypothesis tests and confidence interval estimators for p.
72. To produce a confidence interval estimator for the total, we multiply the lower and upper confidence
limits of the interval estimator of p by ____________________.
73. The formula is used to find the ____________________ to estimate a population
proportion.
74. The formula is used to find the sample size needed to estimate a population
proportion. In this formula, B represents the ____________________ on the error of estimation.
Socialist Party Voters
A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are
Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H0: p = 0.05 vs. H1: p <
0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40.
75. {Socialist Voters Narrative} Test the hypotheses at the 5% significance level.
76. {Socialist Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.
77. {Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population
proportion and explain how to use it to test the hypotheses.
Physicians
A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a
year.
78. {Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of
physicians in the population who make at least $400,000 a year is less than 0.24?
79. {Physicians Narrative} Compute the p-value and explain how to use it to test the hypotheses.
80. {Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of
physicians who make at least $400,000 a year, and explain how to use it to test the hypotheses.
Pilots’ Union Contract
A union composed of several thousand pilots is preparing to vote on a new contract. A random sample
of 500 pilots yielded 320 who planned to vote yes. It is believed that the new contract will receive
more than 60% yes votes.
81. {Pilots’ Union Contract Narrative} State the appropriate null and alternative hypotheses.
82. {Pilots’ Union Contract Narrative} Can we infer at the 5% significance level that the new contract will
receive more than 60% yes votes?
83. {Pilots’ Union Contract Narrative} Compute the p-value for the test.
New Mousetrap
After a financial analysis, the general manager of a large company decided that if more than 8% of
potential buyers of a new mousetrap purchase that product, the company would show a profit. In a
preliminary survey of 500 potential buyers, 56 people say that they will buy the mousetrap.
84. {New Mousetrap Narrative} State the appropriate null and alternative hypotheses.
85. {New Mousetrap Narrative} Is there sufficient evidence at the 5% significance level that the
mousetrap will produce a profit?
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical
studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
86. {Sinus Drug Narrative} We want to test their claim and find out whether the actual percentage is not
10%. State the appropriate null and hypotheses.
87. {Sinus Drug Narrative} Is there enough evidence at the 5% significance level to infer that the
competitor is correct?
88. {Sinus Drug Narrative} Compute the p-value of the test.
89. {Sinus Drug Narrative} Construct a 95% confidence interval estimate of the population proportion of
the users of this allergy drug who experience drowsiness.
90. {Sinus Drug Narrative} Explain how to use this confidence interval to test the hypotheses.
91. As a manufacturer of guitars, a major corporation wants to estimate the proportion of guitar players
who are right-handed. How many golfers must be surveyed if they want to be within 0.02, with a 95%
confidence?
a.
b.
92. In market segmentation, if education is the segmentation variable of interest, then possible segments of
the market include: some high school, high school graduates, some college, college or university
graduates.
93. Market segmentation separates consumers of a product into different groups in such a way that
members of each group are similar to each other and there are differences between groups.
94. Mass Marketing refers to the mass production and marketing by a company of a single product for the
entire market.
95. Generally speaking, mass marketing has given way to target marketing, which focuses on satisfying
the demands of a particular segment of the entire market.
96. Mass marketing refers to the mass production and marketing by a company of all products the
company produces for a single segment of the entire market.
97. Target marketing focuses on satisfying the demands of all segments of the entire market.
98. In estimating the total of a population of size N, where N is very large compared to the sample size, the
confidence interval estimator of the total is .
99. In estimating the population mean
when the population size N is small, the confidence interval
estimator of
is .
100. When is the finite population correction used?
a.
When the population is more than or equal to 20 times the sample size.
b.
When the population is less than or equal to 20 times the population size.
c.
When the population is equal to 20 times the population size.
d.
Whenever the sample size is small, no matter what the population size is.
101. If the lower and upper confidence limits of the population proportion p, using a sample of size 1500,
are 0.184 and 0.238, respectively, then the lower and upper confidence limits of the total number of
successes in the population, given that the population size is 750,000, are respectively:
a.
276 and 357
b.
137,724 and 178,143
c.
138,000 and 178,500
d.
138,276 and 179,857
102. Which of the following statements is correct regarding mass marketing?
a.
It refers to the mass production and marketing by a company of a single product for the
entire market.
b.
It is especially effective for commodity goods such as gasoline, which are very difficult to
differentiate from the competition, except through price and convenience of availability.
c.
Generally speaking, mass marketing has given way to target marketing, which focuses on
satisfying the demands of a particular segment of the entire market.
d.
All of these choices are true.
103. If the lower and upper confidence limits of the population mean
, using a sample of size 100, are 225
and 280, respectively, then the lower and upper confidence limits of the total of a population of size
3000 are respectively
a.
652,500 and 812,000
b.
675,000 and 840,000
c.
697,500 and 868,000
d.
652,862 and 812,452
104. Which of the following statements is false?
a.
Because there is one single way to segment a market, managers must consider several
variable or characteristics that could be used to identify segments.
b.
Surveys of customers are used to gather data about various aspects of the market.
c.
Statistical techniques are applied to the survey data to define the market segments.
d.
Market segmentation separates consumers of a product into different groups in such a way
that members of each group are similar to each other and there are differences between
groups.
105. To estimate the total number of successes in a large finite population of size N, using a sample of size
n, the confidence interval estimator is:
a.
b.
c.
d.
106. To estimate ____________________ when the population size N is small, the confidence interval
estimator is .
107. ____________________ refers to the mass production and marketing by a company of a single
product for the entire market.
ANS:
108. Mass marketing is especially effective for ____________________ goods such as gasoline, which are
difficult to differentiate from the competition except through price and availability.
109. Marketing segmentation separates consumers of a product into different groups in such a way that
members of each group are ____________________ and there are differences between
____________________.
110. When a population is small relative to the sample size, we must incorporate the
____________________ factor in the calculation of the standard error of estimate of the mean.
111. A population is defined to be small if it is ____________________ than ____________________
times the size of the sample.
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet
consciousness as the segmentation variable. Four segments are developed and coded as follows:
1:
2:
3:
4:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are
categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500
Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated
that they are concerned about eating healthy foods. The most recent information available reveals that
there are 40,256,000 Spanish adults who are 20 and over.
112. {Healthy Foods Narrative} What is the objective of this problem?
113. {Healthy Foods Narrative} What is the parameter we wish to estimate? Explain.
114. {Healthy Foods Narrative} What is the point estimate of the proportion p of Spanish adults who
classify themselves as concerned about eating healthy?
115. {Healthy Foods Narrative} Estimate with 95% confidence the proportion p of Spanish adults who
classify themselves as concerned about eating healthy.
116. {Healthy Foods Narrative} Interpret the confidence interval of p.
117. {Healthy Foods Narrative} Estimate with 95% confidence thee number of Spanish adults who
classify themselves as concerned about eating healthy.
Tractor Dealership
An accountant was performing an audit for a tractor dealership. An auditor wants to examine the
monetary error made by the purchasing order department in the month of July. He decided to randomly
sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each
one. The statistics for this sample were: = $6.0 and s = $17.012.
118. {Tractor Dealership Narrative} Estimate with 95% confidence the average amount of error per
purchase order for the entire month of July.
119. {Tractor Dealership Narrative} Why should the finite population correction factor (FPCF) be used for
this problem? Explain.
120. {Tractor Dealership Narrative} Estimate with 95% confidence the total amount of monetary error for
the month of July.