Chapter 9 – Hypothesis Tests
a.
less than or equal to
b.
less than or equal to 2α
c.
greater than or equal to
d.
greater than or equal to 2α
a
78. If a hypothesis test has a Type I error probability of .05, that means
a.
if the null hypothesis is false, it will not be rejected 5% of the time
b.
if the null hypothesis is false, it will be rejected 5% of the time
c.
if the null hypothesis is true, it will not be rejected 5% of the time
d.
if the null hypothesis is true, it will be rejected 5% of the time
79. For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value i
a.
.0101
b.
.0202
c.
.0404
d.
.4899
c
80. The rejection region for a one-tailed hypothesis test
a.
has an area of 1 –
b.
has an area equal to the confidence coefficient
c.
is in the tail that supports the alternative hypothesis
d.
is in the tail that supports the null hypothesis
c
81. The smaller the p-value,
a.
the greater the evidence against H0
b.
the greater the chance of committing a Type II error
c.
the greater the chance of committing a Type I error
d.
the less likely you are to reject H0
a
82. Regarding the Drug and Food Administration’s drug approval process,
a.
the possibility of making a costly error cannot be eliminated if a decision is made
b.
the possibility of a Type I error is eliminated by approving a new drug
c.
the possibility of a Type II error is eliminated by not approving a new drug
d.
the null hypothesis states that the new drug is not safe or effective
Chapter 9 – Hypothesis Tests
a
1
83. “Do not reject H0” is preferred over “Accept H0” because
a.
the conclusion to accept H0 puts us at risk of making a Type I error
b.
the conclusion to reject H0 puts us at risk of making a Type II error
c.
the conclusion to not reject H0 puts us at risk of neither a Type I or Type II error
d.
the conclusion to accept H0 puts us at risk of a Type II error
d
1
84. The equality part of the expression (in either <, >, or =)
a.
always appears in the null hypothesis
b.
always appears in the alternative hypothesis
c.
can appear in either the null or alternative hypothesis
d.
only appears in two-tail hypothesis tests
a
1
85. The p-value approach to hypothesis testing and the critical value approach
a.
are meant for one-tail and two-tail tests, respectively
b.
might or might not lead to the same rejection decision
c.
will always lead to the same rejection decision
d.
cannot lead to the same rejection decision
c
1
86. Statisticians suggest, as a guideline, that a p-value less than .01 be interpreted as _______ evidence to conclude that
Ha is true.
a.
insufficient
b.
weak
c.
strong
d.
overwhelming
d
1
Subjective Short Answer
87. A researcher is testing a new painkiller that claims to relieve pain in less than 15 minutes, on average.
a.
State the hypotheses associated with the researcher’s test.
b.
Describe a Type I error for this situation.
c.
Describe a Type II error for this situation.
88. At a certain manufacturing plant, a machine produced ball bearings that should have a diameter of 0.50 mm. If the
machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a
quality control manager takes a random sample of 30 ball bearings to test to see if the process is “out of control” (i.e. to
test to see if the average diameter differs from 0.50 mm).
a.
State the hypotheses associated with the manager’s test.
b.
Describe a Type I error for this situation.
c.
Describe a Type II error for this situation.
89. A fast food restaurant is considering a promotion that will offer customers to purchase a toy featuring a cartoon movie
character. If more than 20% of the customers purchase the toy, the promotion will be profitable. A sample of 50
restaurants is used to test the promotion.
a.
State the hypotheses associated with the restaurant’s test.
b.
Describe a Type I error for this situation.
c.
Describe a Type II error for this situation.
profitable when more than 20% of customers would purchase the toy.
90. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in
production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this
belief, we randomly selected a sample of 36 of the company’s gas stations and determined that the average price for the
stations in the sample was $1.10. Assume that the standard deviation of the population (σ) is $0.12.
a.
State the null and the alternative hypotheses.
b.
Test the claim at ∝ = .05.
c.
What is the p-value associated with the above sample results?
c.
almost zero
91. “D” size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved
production process, the company believes that there has been an increase in the life expectancy of its “D” size batteries. A
sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the
standard deviation of the population is 9 hours.
a.
Use a 0.01 level of significance, and test to determine if there has been an increase in the life
expectancy of the “D” size batteries.
b.
What is the p-value associated with the sample results? What is your conclusion, based on the
p-value?
92. At a local university, a sample of 49 evening students was selected in order to determine whether the average age of
the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The
population standard deviation is known to be 3.5 years. Determine whether or not the average age of the evening students
is significantly different from 21. Use a 0.1 level of significance.
93. In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was
determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be
$16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from
$108.50.
94. A sample of 81 account balances of a credit company showed an average balance of $1,200. The population standard
deviation is $126. You want to determine if the mean of all account balances is significantly different from $1,150. Use a
.05 level of significance.
95. A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the
average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is
determined that the average length of the bars in the sample is 6.08 centimeters. The population standard deviation is 0.44
centimeters. Determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance.
perfect adjustment.
96. Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway
driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars
average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the
automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per
gallon.
a.
With a 0.05 level of significance, test to determine whether or not the manufacturer’s
advertising campaign is legitimate.
b.
What is the p-value associated with the sample results?
b.
97. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers
is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be
5.6 days.
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the null hypothesis at the 5% level of significance.
c.
Using a p-value, test the hypothesis at the 5% level of significance.
d.
What type of error may have been committed for this hypothesis test?
98. A student believes that the average grade on the statistics final examination is 87. A sample of 36 final examinations is
taken. The average grade in the sample is 83.96. The population variance is 144.
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the hypothesis at the 5% level of significance.
c.
Using a p-value, test the hypothesis at the 5% level of significance.
d.
Using a confidence interval, test the hypothesis at the 5% level of significance.
e.
Compute the probability of a Type II error if the average grade on the final is 85.
e.
99. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers
is taken. The average delivery time in the sample was 16.2 days. The population standard deviation is 5.6 days.
Chapter 9 – Hypothesis Tests
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the null hypothesis at the 5% level of significance.
c.
Using a p-value, test the hypothesis at the 5% level of significance.
d.
Compute the probability of a Type II error if the true average delivery time is 17 days after
purchase.
d.
0.1949
100. The sponsors of televisions shows targeted at the market of 5 – 8 year olds want to test the hypothesis that children
watch television at most 20 hours per week. The population of viewing hours per week is known to be normally
distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this
age group. The resulting data follows:
19.5
29.7
17.5
10.4
19.4
18.4
14.6
10.1
12.5
18.2
19.1
30.9
22.2
19.8
11.8
19.0
27.7
25.3
27.4
26.5
16.1
21.7
20.6
32.9
27.0
15.6
17.1
19.2
20.1
17.7
At a .10 level of significance, use Excel to test the sponsors’ hypothesis.
101. At a certain manufacturing plant, a machine produces ball bearings that should have a diameter of 0.500 mm. If the
machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a
quality control manager takes a random sample of 36 ball bearings to test to see if the process is “out of control” (i.e. to
test to see if the average diameter differs from 0.500 mm). Assume that the process is maintaining the desired standard
deviation of .06 mm. The results from the latest sample follow:
0.468
0.521
0.421
0.476
0.448
0.346
0.452
0.513
0.465
0.395
0.558
0.526
0.354
0.474
0.447
0.405
0.411
0.453
0.456
0.477
0.529
0.440
0.570
0.319
0.471
0.480
0.499
0.446
0.405
0.557
0.468
0.521
0.421
0.476
0.448
0.346
At a .01 level of significance, use Excel to test whether the process is “out of control.”
102. From a population of cans of coffee marked “12 ounces,” a sample of 25 cans is selected and the contents of each can
are weighed. The sample revealed a mean of 11.8 ounces and a standard deviation of 0.5 ounces. Test to see if the mean of
the population is at least 12 ounces. (Assume the population is normally distributed.) Use a .05 level of significance.
103. In the past the average age of employees of a large corporation has been 40 years. Recently, the company has been
hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees,
a sample of 25 employees was selected. The average age in the sample was 45 years with a standard deviation of 5 years.
Assume the distribution of the population is normal. Let α = .05.
a.
State the null and the alternative hypotheses.
b.
Test to determine whether or not the mean age of all employees is significantly more than 40
years.
104. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random
sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with
a standard deviation of 0.24 ounces. With a 0.05 level of significance, test to see if the machine is in perfect adjustment.
Chapter 9 – Hypothesis Tests
Assume the distribution of the population is normal.
105. A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average
number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of
the population is normal.
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the hypothesis at the 1% level of significance.
c.
Using a p-value, test the hypothesis at the 1% level of significance.
d.
Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.
106. Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and
the following running times were obtained. Assume the distribution of the population is normally distributed.
150
150
180
170
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the hypothesis at the 10% level of significance.
c.
Using a p-value, test the hypothesis at the 10% level of significance.
d.
Using a confidence interval, test the hypothesis at the 10% level of significance.
e.
Could a Type II error have been committed in this hypothesis test?
107. You are given the following information obtained from a random sample of 5 observations.
20
18
17
22
18
At a 10% level of significance, use Excel to determine whether or not the mean of the population from which this sample
was taken is significantly less than 21. (Assume the population is normally distributed.)
108. You are given the following information obtained from a random sample of 4 observations.
25
47
32
56
At a .05 level of significance, use Excel to determine whether or not the mean of the population from which this sample
was taken is significantly different from 48. (Assume the population is normally distributed.)
=COUNT(A2:A5)
25
=AVERAGE(A2:A5)
40
47
=STDEV(A2:A5)
14.07125
32
56
48
48
=D3/SQRT(D1)
7.03562
=(D2-D5)/D7
-1.13707
=T.DIST(D8,D9,TRUE)
0.16906
0.83094
=2*MIN(D11,D12)
0.33811
109. A group of young businesswomen wish to open a high fashion boutique in a vacant store, but only if the average
income of households in the area is more than $45,000. A random sample of 9 households showed the following results.
$48,000
$44,000
$46,000
$43,000
$47,000
$46,000
$44,000
$42,000
$45,000
20
=AVERAGE(A2:A6)
19
18
=STDEV(A2:A6)
17
22
21
21
18
=D3/SQRT(D1)
0.8944272
=(D2-D5)/D7
-2.236068
=T.DIST(D8,D9,TRUE)
0.04450
0.95550
=2*MIN(D11,D12)
0.08901
Chapter 9 – Hypothesis Tests
Use the statistical techniques in Excel to advise the group on whether or not they should locate the boutique in this store.
Use a .05 level of significance. (Assume the population is normally distributed.)
110. In a television commercial, the manufacturer of a toothpaste claims that at least 4 out of 5 dentists recommend its
product. A consumer-protection group wants to test that claim. Identify the hypotheses.
111. A manufacturer is considering a new production method. The current method produces 94% non-defective (good)
parts. The new method will be implemented if it produces more non-defectives than the current method. Identify the
hypotheses.
112. Consider the following hypothesis test:
Ho: p = 0.5
Ha: p ≠ 0.5
A sample of 800 provided a sample proportion of 0.58.
a.
Using α = 0.05, what is the rejection rule?
b.
Determine the standard error of the proportion.
c.
Compute the value of the test statistic z. What is your conclusion?
d.
Determine the p-value.
Reject H0 if z ≤ -1.96 or if z ≥ 1.96
b.
4.53; reject H0, there is sufficient evidence at α = .05 to conclude that the population proportion
POINTS:
1
113. A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated
they like the taste.
a.
At a 5% significance level, test to determine if at least 22% of the population will like the new
soft drink.
b.
Determine the p-value.
b.
POINTS:
1
114. A student believes that no more than 20% (i.e., ≤ 20%) of the students who finish a statistics course get an A. A
random sample of 100 students was taken. Twenty-four percent of the students in the sample received A’s.
a.
State the null and alternative hypotheses.
b.
Using a critical value, test the hypothesis at the 1% level of significance.
c.
Using a p-value, test the hypothesis at the 1% level of significance.
POINTS:
1
115. For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A
large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds
that 6 parts are defective. Is this sufficient evidence to reject the entire shipment? Use a .05 level of significance to
conduct the appropriate hypothesis test.
POINTS:
1
116. A national poll reported that 58% of those with Internet access have made purchases online. To investigate whether
this percentage applies to its own state, a legislator commissions a study. A random sample of 400 state residents who
have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample
provide sufficient evidence to conclude that the state differs from the nation with respect to making purchases online? Use
the p-value to conduct the hypothesis test and use a .05 level of significance.
117. An official of a large national union claims that the fraction of women in the union is not significantly different from
one-half. Using the sample information reported below, carry out a test of this statement. Use a .05 level of significance.
d.
Chapter 9 – Hypothesis Tests
sample size
400
women
168
men
232
1
118. A manufacturer claims that at least 40% of its customers use coupons. A study of 25 customers is undertaken to test
that claim. The results of the study follow.
yes
no
no
yes
yes
no
yes
no
no
yes
no
no
no
no
yes
no
no
no
no
yes
no
no
yes
no
yes
At a .05 level of significance, use Excel to test the manufacturer’s claim.
1
119. Several years ago the proportion of Americans aged 18 – 24 who invested in the stock market was 0.20. A random
sample of 25 Americans in this age group was recently taken. They were asked whether or not they invested in the stock
market. The results follow:
yes
no
no
yes
no
no
yes
no
no
yes
no
no
no
no
no
no
no
no
yes
no
no
no
yes
no
no
At a .05 level of significance, use Excel to determine whether or not the proportion of Americans 18 – 24 years old that
invest in the stock market has changed.
120. Identify the null and alternative hypotheses for the following problems.
a.
The manager of a restaurant believes that it takes a customer no more than 25 minutes to eat
lunch.
b.
Economists have stated that the marginal propensity to consume is at least 90¢ out of every
dollar.
c.
It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy
popcorn.
121. Fast ‘n Clean operates 12 laundromats on the east side of the city. All of Fast ‘n Clean’s clothes dryers have a label
stating “20 minutes for $1.00.” You question the accuracy of the dryers’ clocks and decide to conduct an observational
study. You randomly select 36 dryers in several different Fast ‘n Clean locations, put $1.00 in each and time the drying
cycle. The sample mean drying time is 20 minutes and 25 seconds. The manufacturer of the dryer states that the standard
deviation for 20-minute drying cycles is 1 minute.
a. Using the sample data and α = .05, test the validity of the label on the dryers. Apply the p-value and critical value
approaches to conducting the two-tail hypothesis test.
b. Conduct the same two-tail hypothesis test, but this time use the confidence interval approach to hypothesis testing.
122. Laura Naples, Manager of Heritage Inn, periodically collects and tabulates information about a sample of the hotel’s
overnight guests. This information aids her in pricing and scheduling decisions she must make. The table below lists data
on ten randomly selected hotel registrants, collected as the registrants checked out. The data listed are:
• Number of people in the group
• Hotel’s shuttle service used: yes or no
• Total telephone charges incurred
• Reason for stay: business or personal
Name of
Registrant
Number in
Group
Shuttle
Used
Telephone
Charges ($)
Reason for
Stay
Madam Sandler
1
yes
0.00
personal
Michelle Pepper
2
no
8.46
business
Claudia Shepler
1
no
3.20
business
Annette Rodriquez
2
no
2.90
business
Tony DiMarco
1
yes
3.12
personal
Amy Franklin
3
yes
4.65
business
Julio Roberts
2
no
6.35
personal
Edward Blackstone
4
yes
2.10
personal
Sara Goldman
1
no
1.85
business
Todd Atherton
1
no
5.80
business
a. Before cell telephones became so common, the average telephone charge per registered group was at least $5.00.
Laura suspects that the average has dropped. Test H0:
> 5 and Ha:
< 5 using a .05 level of significance. Use both the
critical value and p-value approaches to hypothesis testing.
b. In the past, Laura has made some important managerial decisions based on the assumption that the average number of
people in a registered group is 2.5. Now she wonders if the assumption is still valid. Test the assumption with α = .05
and use both the critical value and p-value approaches.
123. The board of directors of a corporation has agreed to allow the human resources manager to move to the next step in
planning day care service for employees’ children if the manager can prove that at least 25% of the employees have
interest in using the service. The HR manager polls 300 employees and 90 say they would seriously consider utilizing the
service. At the α = .10 level of significance, is there enough interest in the service to move to the next planning step?
yes, there is enough interest to move to the next step
124. A radio talk show host in Brockdale has complained that the average monthly rent for an efficiency apartment in that
city is $600 or more. The Brockdale Landlords Association (BLA) believes that this claim is an exaggeration. BLA takes
a random sample of 100 efficiency apartments in the city, inquiring about the monthly rent charged for each. The mean
Chapter 9 – Hypothesis Tests
rent for the 100-apartment sample is $592. Conduct a hypothesis test with
= .05 and draw your conclusion using the p–
value approach. (Assume the standard deviation for all efficiency apartment rents in this city is known to be about $52.)