Chapter 12: More about Tests and Intervals – Quiz A
Name ________________________________________
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
1. Your company has developed a new auto fuel additive that you can claim increases a
car’s gas mileage. You test it on a random sample of cars under a random sample of
driving conditions and find that the cars you tested did have somewhat better gas mileage
than normal.
a. This difference in gas mileage can be the result of one of two things. State the two
specific reasons.
b. Explain what a Type I error would mean in this example.
c. Explain what a Type II error would mean in this example.
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
2. Suppose a researcher conducts an experiment to test a hypothesis. If she doubles her
sample size, how will that affect the power of the test, the effect size of the test or the
probability of making a Type II error?
12.4.3 Construct confidence intervals and perform hypothesis tests.
3. May’s Consignment Shop want to know whether 25% or more of the customers will
spend $200 or more in the next month and qualify for a special program. We will use the
data from the same month a year ago to estimate the proportion and see whether the
proportion was at least 25%. The proportion of customers who charged $200 or more was
0.280.
a. What are the 4 conditions that need to be checked?
b. What are the hypotheses for this test?
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
4. A company that sells eco-friendly cleaning products is concerned that only 19.5% of
people who use such products select their brand. A marketing director suggests that the
company invest in new advertising and labeling to strengthen its green image. The
company decides to do so in a test market so that the effectiveness of the marketing
campaign may be evaluated.
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact the
company?
c. In this context, describe the Type II error possible. How might such an error impact
the company?
d. Based on data collected in the test market, the company constructed a 98% confidence
interval for the proportion of all consumers who might buy their brand. The resulting
interval is 16% to 28%. What conclusion should the company reach about the new
marketing campaign? Explain.
12-2 Chapter 12 More about Tests and Intervals
Chapter 12: More about Tests and Intervals – Quiz A – Key
Quiz A 12-3
12-4 Chapter 12 More about Tests and Intervals
Quiz B 12-5
Chapter 12: More about Tests and Intervals – Quiz B
Name ________________________________________
12.4.3 Construct confidence intervals and perform hypothesis tests.
1. A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They
believe that the firm’s professionals volunteer an average of more than 15 hours per
month. If this is not the case, they will institute an incentive program to increase
community involvement. A random sample of 24 professionals reported the following
number of hours:
12 13 14 14 15 15 15 16 16 16 16 16
17 17 17 18 18 18 18 19 19 19 20 21
The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours.
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact the
software development firm?
c. In this context, describe the Type II error possible. How might such an error impact
the software development firm?
d. What is the value of the test statistic?
e. What is the associated P-value?
f. State your conclusion using α = .05.
12.4.3 Construct confidence intervals and perform hypothesis tests.
2. Top management of a large multinational corporation wants to create a culture of
innovativeness and change. A consultant hired to assess the company’s organizational
culture finds that only 15% of employees are open to new ideas and approaches toward
their work. One of his recommendations is for the company to conduct seminars for
employees in order to disseminate and reinforce the new corporate philosophy. This is
done for a six month trial period after which its value in changing employee attitudes will
be assessed.
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact the
company?
c. In this context, describe the Type II error possible. How might such an error impact
the company?
d. Based on data collected after the trial period, the company constructed a 95%
confidence interval for the proportion of all employees open to new ideas and approaches
toward their work. The resulting interval is 18% to 22%. What conclusion should the
company reach about the seminars? Explain.
12-6 Chapter 12 More about Tests and Intervals
12.4.3 Construct confidence intervals and perform hypothesis tests.
3. Insurance companies track life expectancy information to assist in determining the
cost of life insurance policies. Last year the average life expectancy of all policyholders
was 77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample some of their recently paid policies.
The insurance company will only change their premium structure if there is evidence that
people who buy their policies are living longer than before. The sample has a mean of
78.6 years and a standard deviation of 4.48 years.
86 75 83 84 81 77 78 79 79 81
76 85 70 76 79 81 73 74 72 83
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact
ABI Insurance?
c. In this context, describe the Type II error possible. How might such an error impact
ABI Insurance?
d. What is the value of the test statistic?
e. What is the associated P-value?
12.4.3 Construct confidence intervals and perform hypothesis tests.
4. Construct a 95% confidence interval for the true proportion using 100 as a sample size
using a sample proportion of 0.30. If a hypothesized proportion is 0.20, draw a
conclusion based on this interval.
Quiz B 12-7
Chapter 12: More about Tests and Intervals – Quiz B – Key
12-8 Chapter 12 More about Tests and Intervals
Quiz B 12-9
12-10 Chapter 12 More about Tests and Intervals
Quiz C 12-11
Chapter 12: More about Tests and Intervals – Quiz C – Multiple Choice
Name ________________________________________
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
1. A company that sells eco-friendly cleaning products is concerned that only 19.5% of
people who use such products select their brand. A marketing director suggests that the
company invest in new advertising and labeling to strengthen its green image. The
company decides to do so in a test market so that the effectiveness of the marketing
campaign may be evaluated. In this context, committing a Type I error
A. Occurs when they conclude that the percentage of customers purchasing the
company’s brand has increased when in fact it has not.
B. Occurs then they conclude that the percentage of customers purchasing the
company’s brand has not increased when in fact it has.
C. Would result in the company wasting money on a new marketing campaign that does
not increase the percentage of customers buying their brand.
D. Both A and C.
E. Both B and C.
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
2. A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They
believe that the firm’s professionals volunteer an average of more than 15 hours per
month. If this is not the case, they will institute an incentive program to increase
community involvement. Based on data collected they perform the appropriate
hypothesis test. A Type II error in this context means
A. They failed to detect that the average number of hours volunteered by the firm’s
professional employees is more than 15 hours when in fact it is.
B. They would decide not to institute an incentive program to increase community
involvement when they should have.
C. They would waste money instituting an incentive program to increase community
involvement among its professional employees that was not needed.
D. Both A and B.
E. Both A and C.
12-12 Chapter 12 More about Tests and Intervals
12.4.3 Construct confidence intervals and perform hypothesis tests.
3. In a metal fabrication process, metal rods are produced to a specified target length of
15 feet. Suppose that the lengths are normally distributed. A quality control specialist
collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
a standard deviation of 0.65 feet. The 95% confidence interval for the true mean length
of rods produced by this process is
A. 14.544 to 15.056 ft.
B. 14.345 to 15.255 ft.
C. 13.912 to 15.688 ft.
D. 14.454 to 15.146 ft.
E. 13.834 to 15.766 ft.
12.3.2. Find critical values and make conclusions.
4. A manufacturer of cream filled donuts collected data from its automatic filling process,
the amount of cream inserted into the donuts is normally distributed. To make sure that
the automatic filling process is on target, quality control inspectors take a sample of 25
donuts. The correct value of t* to construct a 99% confidence interval for the true mean
amount of cream filling is
A. 2.797
B. 1.711
C. 2.787
D. 2.060
E. 1.318
12.4.3 Construct confidence intervals and perform hypothesis tests.
5. A manufacturer of cream filled donuts collected data from its automatic filling process,
the amount of cream inserted into the donuts is normally distributed. To make sure that
the automatic filling process is on target, quality control inspectors take a sample of 25
donuts and measure the weight of cream filling. They find a sample mean weight of 15
grams with a standard deviation of 1.5 grams. What is the margin of error at 90%
confidence?
A. 0.3 grams
B. 0.5133 grams
C. 0.8391 grams
D. 1.5 grams
E. 0.06 grams
Quiz C 12-13
12.4.3 Construct confidence intervals and perform hypothesis tests.
6. Insurance companies track life expectancy information to assist in determining the cost
of life insurance policies. ABI Insurance randomly sampled 100 recently paid policies
and determined the average age of clients in this sample to be 77.7 years with a standard
deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance
policy holders is
A. 77.1 to 78.3 years
B. 76.87 to 80.33 years
C. 75.4 to 80 years
D. 74.1 to 81.3 years
E. 72.5 to 82.9 years
12.4.3 Construct confidence intervals and perform hypothesis tests.
7. Which of the following is not an assumption and/or condition required for constructing
a confidence interval for the mean?
A. Randomization condition
B. Nearly Normal condition
C. Success/Failure condition
D. 10% condition
E. Independence assumption
12.4.3 Construct confidence intervals and perform hypothesis tests.
8. A manufacturer of cream filled donuts collected data from its automatic filling process,
the amount of cream inserted into the donuts is normally distributed. To make sure that
the automatic filling process is on target, quality control inspectors take a sample of 25
donuts and measure the weight of cream filling. They find the 99% confidence interval
of 14.16 to 15.84 grams. Which of the following is the correct interpretation?
A. We are 99% confident that the mean weight of cream filling in all donuts made by this
process is between 14.16 and 15.84 grams.
B. 99% of all donuts made by this process will have cream filling weights between 14.16
and 15.84 grams.
C. The weight of cream filling in the donuts is between 14.16 and 15.84 grams 99% of
the time.
D. All of the above.
E. None of the above.
12-14 Chapter 12 More about Tests and Intervals
12.3.2. Find critical values and make conclusions.
9. A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They
believe that the firm’s professionals volunteer an average of more than 15 hours per
month. If this is not the case, they will institute an incentive program to increase
community involvement. A random sample of 24 professionals yields a mean of 16.6
hours and a standard deviation of 2.22 hours. The correct value of the test statistic for the
appropriate hypothesis test is
A. t = 3.532
B. t = -3.532
C. t = 1.223
D. t = -1.223
E. t = 0.789
12.1.1. Interpret and understand P‐values and alpha levels.
10. A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They
believe that the firm’s professionals volunteer an average of more than 15 hours per
month. If this is not the case, they will institute an incentive program to increase
community involvement. A random sample of 24 professionals yields a mean of 16.6
hours and a standard deviation of 2.22 hours. The P-value associated with the resulting
test statistic is 0.0009. At α = 0.05, which of the following is the correct conclusion?
A. We reject the null hypothesis.
B. We fail to reject the null hypothesis.
C. The firm shouldn’t need to institute an incentive program because the evidence
indicates that professional employees volunteer an average of more than 15 hours per
month in their local community.
D. Both A and C.
E. Both B and C.
Quiz C 12-15
Chapter 12: More about Tests and Intervals – Quiz C – Key
12-16 Chapter 12 More about Tests and Intervals
Chapter 12: More about Tests and Intervals – Quiz D – Multiple Choice
Name ________________________________________
12.1.3 Construct confidence intervals and perform hypothesis tests.
1. A report on the U.S. economy indicates that 28% of Americans have experienced
difficulty in making mortgage payments. A news organization randomly sampled 400
Americans from 10 cities named the “fastest dying cities in the U.S.” (Forbes Magazine,
August 2008) and found that 136 reported such difficulty. Does this indicate that the
problem is more severe among these cities? The correct null and alternative hypotheses
for testing this claim are
A. H0 : p = 0.28 and HA : p > 0.28
B. H0 : p = 0.28 and HA : p < 0.28
C. H0 : p = 0.28 and HA : p ≠ 0.28
D. H0 : p ≠ 0.28 and HA : p = 0.28
E. H0 : p > 0.28 and HA : p = 0.28
12.3.2. Find critical values and make conclusions.
2. A report on the U.S. economy indicates that 28% of Americans have experienced
difficulty in making mortgage payments. A news organization randomly sampled 400
Americans from 10 cities named the “fastest dying cities in the U.S.” (Forbes Magazine,
August 2008) and found that 136 reported such difficulty. Does this indicate that the
problem is more severe among these cities? The correct value of the test statistic for
testing this claim is
A. z = -1.28
B. z = -2.67
C. z = 2.67
D. z = 1.96
E. z = -1.28
12.4.3 Construct confidence intervals and perform hypothesis tests.
3. A small business ships specialty homemade candies to anywhere in the world. Past
records indicate that the weight of orders is normally distributed. Suppose a random
sample of 16 orders is selected and each is weighed. The sample mean was found to be
110 grams with a standard deviation of 14 grams. The 90% confidence interval for the
true mean weight of orders is
A. 103.87 to 116.14 grams.
B. 86.046 to 133.954 grams.
C. 99.5 to 120.5 grams.
D. 102.55 to 117.45 grams.
E. 103.14 to 116.86 grams.
Quiz D 12-17
12.3.2. Find critical values and make conclusions.
4. Grandma Gertrude’s Chocolates, a family owned business, has an opportunity to
supply its product for distribution through a large coffee house chain. However, the
coffee house chain has certain specifications regarding cacao content as it wishes to
advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
pieces. They find a sample mean of 55% with a standard deviation of 4%. The correct
value of t* to construct a 90% confidence interval for the true mean % cacao is
A. 2.797
B. 1.711
C. 1.690
D. 2.030
E. 1.318
12.4.3 Construct confidence intervals and perform hypothesis tests.
5. Top management of a large multinational corporation wants to create a culture of
innovativeness and change. A consultant hired to assess the company’s organizational
culture finds that only 15% of employees are open to new ideas and approaches toward
their work. Consequently the company conducts a program for employees in order to
reinforce the new corporate philosophy. After the program is completed, employees are
surveyed to see if a greater percentage is now open to innovativeness and change. The
correct alternative hypothesis is
A. p = 0.15
B. p > 0.15
C. p < 0.15
D. µ > 0.15
E. µ ≠ 0.15
12.1.1. Interpret and understand P‐values and alpha levels.
6. Insurance companies track life expectancy information to assist in determining the cost
of life insurance policies. Last year the average life expectancy of all policyholders was
77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample 20 of their recently paid policies. The
sample has a mean of 78.6 years and a standard deviation of 4.48 years. The P-value
associated with the resulting test statistic is 0.063. At α = 0.05, which of the following is
the correct conclusion?
A. We fail to reject the null hypothesis.
B. We reject the null hypothesis.
C. There is not significant evidence to indicate an increase in average life expectancy.
D. Both A and C.
E. Both B and C.
12-18 Chapter 12 More about Tests and Intervals
12.1.1. Interpret and understand P‐values and alpha levels.
7. A report on the U.S. economy indicates that 28% of Americans have experienced
difficulty in making mortgage payments. A news organization randomly sampled 400
Americans from 10 cities named the “fastest dying cities in the U.S.” (Forbes Magazine,
August 2008) and found that 136 reported such difficulty. Does this indicate that the
problem is more severe among these cities? The P-value associated with the test statistic
for testing this claim is 0.0029. At α = .05,
A. We can conclude that the percentage of Americans in these cities experiencing
difficulty making mortgage payments is significantly higher than 28%.
B We can conclude that the percentage of Americans in these cities experiencing
difficulty making mortgage payments is significantly lower than 28%.
C. We can conclude that the percentage of Americans in these cities experiencing
difficulty making mortgage payments is not significantly different from 28%.
D. We can conclude that the percentage of Americans in these cities experiencing
difficulty making mortgage payments is equal to 28%.
E. None of the above.
12.3.2 Find critical values and make conclusions.
8. Suppose that you are conducting a two tailed test about a proportion at the 0.01 level
of significance. The correct critical value(s) to be used in drawing a conclusion is (are)
A. ± 1.96
B. ±2.575
C. -1.645
D. ±1.645
E. 1.96
12.4.3 Construct confidence intervals and perform hypothesis tests.
9. Insurance companies track life expectancy information to assist in determining the cost
of life insurance policies. Last year the average life expectancy of all policyholders was
77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample some of their recently paid policies.
The insurance company will only change their premium structure if there is evidence that
people who buy their policies are living longer than before. Which of the following
statement is true about this hypothesis test?
A. It is a two tailed test about a proportion.
B. It is a one tailed test about a mean.
C. It is a one tailed test about a proportion.
D. It is a two tailed test about a mean.
E. None of the above.
Quiz D 12-19
12.5.4 Identify and understand Type I errors, Type II errors, and the power of a test.
10. Top management of a large multinational corporation wants to create a culture of
innovativeness and change. A consultant hired to assess the company’s organizational
culture finds that only 15% of employees are open to new ideas and approaches toward
their work. Consequently the company conducts a program for employees in order to
reinforce the new corporate philosophy. After the program is completed, employees are
surveyed to see if a greater percentage is now open to innovativeness and change.
Suppose that based on the sample results the company rejects the null hypothesis when in
fact it is true. Which of the following statements is correct?
A. This is known as a Type II error.
B. This is known as a fatal error.
C. This led to the conclusion that the percentage of employees open to new ideas did not
increase when in fact it did.
D. This led to the conclusion that the percentage of employees open to new ideas did
increase when in fact it did not.
E. This led to a P-value that was greater than the level of significance.
12-20 Chapter 12 More about Tests and Intervals
Chapter 12: Confidence Intervals for Means – Quiz D – Key