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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9 TEST
FORM A
For each of the following problems, please provide the requested information.
(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed,
right-tailed, or two-tailed test?
(b) Identify the sampling distribution you will use: the standard normal or the Student’s t.
Explain the rationale for your choice. What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to
the P-value.
(d) Find the critical value(s).
(e) Based on your answers for parts (a) to (d), will you reject or fail to reject the null hypothesis?
State your conclusion in the context of the application.
1. A large furniture store has begun a new ad campaign on local television. Before the campaign, the long
term average daily sales were $24,819. A random sample of 40 days during the new ad campaign gave a
sample mean daily sale of x = $25,910. Does this indicate that the population mean daily sales is now
more than $24,819? Use a 1% level of significance. Assume σ = $1917.
1. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Part III: Sample Tests, Chapter 9
129
CHAPTER 9, FORM A, PAGE 2
2. A new bus route has been established between downtown Denver and Englewood, a suburb of Denver.
Dan has taken the bus to work for many years. For the old bus route, he knows from long experience that
the mean waiting time between buses at his stop was µ = 18.3 minutes. However, a random sample of 5
waiting times between buses using the new route had mean x = 15.1 minutes with sample standard
deviation s = 6.2 minutes. Does this indicate that the population mean waiting time for the new route is
different from what it used to be? Use α = 0.05. Assume x is normally distributed.
2. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
3. The State Fish and Game Division claims that 75% of the fish in Homestead Creek are Rainbow Trout.
However, the local fishing club caught (and released) 189 fish one weekend, and found that 125 were
Rainbow Trout. The other fish were Brook Trout, Brown Trout, and so on. Does this indicate that the
percentage of Rainbow Trout in Homestead Creek is less than 75%? Use α = 0.01.
3. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9, FORM A, PAGE 3
4. A telemarketer is trying two different sales pitches to sell a carpet cleaning service. For Sales Pitch I, 175
people were contacted by phone and 62 of these people bought the cleaning service. For Sales Pitch II,
154 people were contacted by phone and 45 of these people bought the cleaning service. Does this
indicate that there is any difference in the population proportions of people who will buy the cleaning
service, depending on which sales pitch is used? Use α = 0.05
4. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
5. A systems specialist has studied the work-flow of clerks all doing the same inventory work. Based on this
study, she designed a new work-flow layout for the inventory system. To compare average production for
the old and new methods, a random sample of six clerks was used. The average production rate (number
of inventory items processed per shift) for each clerk was measured both before and after the new system
was introduced. The results are shown below. Test the claim that the new system increases the mean
number of items process per shift. Use α = 0.05.
Clerk
B: Old
A: New
1
116
123
2
108
114
3
93
112
4
88
82
5
119
127
6
111
122
5. (a)
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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CHAPTER 9, FORM A, PAGE 4
6. How productive are employees? One way to answer this question is to study annual company profits per
employee. Let x1 represent annual profits per employee in computer stores in St. Louis. A random sample
of n1 = 11 computer stores gave a sample mean of x1 = 25.2 thousand dollars profit per employee with
sample standard deviation s1 = 8.4 thousand dollars. Another random sample of n2 = 9 building supply
stores in St. Louis gave a sample mean x2 = 19.9 thousand dollars per employee with sample standard
deviation s2 = 7.6 thousand dollars. Does this indicate that in St. Louis, computer stores tend to have
higher mean profits per employee? Use α = 0.01
6. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
7. How big are tomatoes? Some say that depends on the growing conditions. A random sample of n1 = 89
organically grown tomatoes had sample mean weight x1 = 3.8 ounces. Another random sample of n2 = 75
tomatoes that were not organically grown had sample mean weight x2 = 4.1 ounces. Previous studies
show that σ1 = 0.9 ounce and σ 2 = 1.5 ounces. Does this indicate a difference either way between
population mean weights of organically grown tomatoes compared to those not organically grown? Use a
5% level of significance.
7. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9, FORM A, PAGE 5
8. How tall are college hockey players? The average height has been 68.3 inches. A random sample of
14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution
with σ = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use
5% level of significance.
8. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
9. How long does it take to have food delivered? A Chinese restaurant advertises that delivery will be no
more than 30 minutes. A random sample of delivery times (in minutes) is shown below. Based on this
sample, is the delivery time greater than 30 minutes? Use a 5% level of significance. Assume that the
distribution of times is normal.
32
39
28
32
21
28
39
42
30
25
27
26
29
30
9. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Part III: Sample Tests, Chapter 9
133
CHAPTER 9, FORM A, PAGE 6
10. A music teacher knows from past records that 60% of students taking summer lessons play the piano. The
instructor believes this proportion may have dropped due to the popularity of wind and brass instruments.
A random sample of 80 students yielded 43 piano players. Test the instructor’s claim at α = 0.05.
10. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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134
Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9 TEST
FORM B
For each of the following problems, please provide the requested information.
(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed,
right-tailed, or two-tailed test?
(b) Identify the sampling distribution you will use: the standard normal or the Student’s t.
Explain the rationale for your choice. What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to
the P-value.
(d) Find the critical value(s).
(e) Based on your answers for parts (a) to (d), will you reject or fail to reject the null hypothesis?
State your conclusion in the context of the application.
1. Long term experience showed that after a type of eye surgery it took a mean of µ = 5.3 days recovery time
in a hospital. However, a random sample of 32 patients with this type of eye surgery, were recently
treated as outpatients during the recovery. The sample mean recovery time was x = 4.2 days. Does this
indicate that the mean recovery time for outpatients is less than the time for those recovering in the
hospital? Use a 1% level of significance. Assume σ = 1.9 days.
1. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Part III: Sample Tests, Chapter 9
135
CHAPTER 9, FORM B, PAGE 2
2. Recently the national average yield on municipal bonds has been µ = 4.19%. A random sample of 16
Arizona municipal bonds gave an average yield of 5.11% with sample standard deviation s = 1.15%. Does
this indicate that the population mean yield for all Arizona municipal bonds is greater than the national
average? Use a 5% level of significance. Assume x is normally distributed.
2. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
3. At a local four-year college, 37% of the student-body are freshmen. A random sample of 42 student
names taken from the Dean’s Honor List over the past several semesters showed that 17 were freshmen.
Does this indicate the population proportion of freshmen on the Dean’s Honor List is different from 37%?
Use a 1% level of significance.
3. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
Copyright © Houghton Mifflin Company. All rights reserved.
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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9, FORM B, PAGE 3
4. In a random sample of 62 students, 34 said they would vote for Jennifer as student body president. In
another random sample of 77 students, 48 said they would vote for Kevin as student body president. Does
this indicate that in the population of all students, Kevin has a higher proportion of votes? Use α = 0.05
4. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
5. Five members of the college track team in Denver (elevation 5200 ft) went up to Leadville (elevation
10,152 ft) for a track meet. The times in minutes for these team members to run two miles at each location
are shown below.
Team Member
Denver
Leadville
1
10.7
11.5
2
9.1
10.6
3
11.4
11.0
4
9.7
11.2
5
9.2
10.3
Assume the team members constitute a random sample of track team members. Use a 5% level of
significance to test the claim that the times were longer at the higher elevation.
5. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Part III: Sample Tests, Chapter 9
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CHAPTER 9, FORM B, PAGE 4
6. Two models of a popular pick-up truck are tested for miles per gallon (mpg) gasoline consumption. The
Pacer model was tested using a random sample of n1 = 9 trucks and the sample mean was x1 = 27.3 mpg
with sample standard deviation s1 = 6.2 mpg. The Road Runner model was tested using a random sample
of n2 = 14 trucks. The sample mean was x2 = 22.5 mpg with sample standard deviation s2 = 6.8 mpg.
Does this indicate that the population mean gasoline consumption for the Pacer is higher than that of the
Road Runner? Use α = 0.01
6. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
7. Students at the college agricultural research station are studying egg production of range free chickens
compared to caged chickens. During a one week period, a random sample of n1 = 93 range free hens
produced an average of x1 = 11.2 eggs. For the same period, another random sample of n2 = 87 caged
hens produced a sample average of x2 = 8.5 eggs per hen. Previous studies show that σ1 = 4.4 eggs and
σ 2 = 5.7 eggs. Does this indicate the population mean egg production for range free hens is higher? Use
a 5% level of significance.
7. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9, FORM B, PAGE 5
8. How long does it take juniors to complete a standardized exam? The long-term average is 2.8 hours. We
may assume that x has a normal distribution with σ = 0.8 hour. A random sample of 12 juniors gave a
sample mean of x = 2.2 hours. Does this indicate that the population mean time is different from
2.8 hours? Use 5% level of significance.
8. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
9. How old are the customers? The owner of a comedy club has based business decisions on the average of
customers historically being 30 years. A random sample of customers’ ages (in years) is shown below.
Based on this sample, is the average age more than 30 years? Use a 5% level of significance. Assume
that the distribution of ages is normal.
37
43
30
27
26
39
35
38
45
46
42
21
51
28
40
20
9. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Part III: Sample Tests, Chapter 9
139
CHAPTER 9, FORM B, PAGE 6
10. The Department of Transportation in a particular city knows from past records that 27% of workers in the
downtown district use the subway system each day to commute to or from work. The department suspects
this proportion has increased due to decreased parking spaces in the downtown district. A random sample
of 130 workers in the downtown district showed 49 used the subway daily. Test the departments’
suspicion at the 5% level of significance.
10. (a) __________________________
(b) __________________________
(c)
(d) __________________________
(e) __________________________
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Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9 TEST
FORM C
Write the letter of the response that best answers each problem.
1. A small electronics store has begun to advertise in the local newspaper. Before advertising, the long term
average weekly sales were $9820. A random sample of 50 weeks while the newspaper ads were running
gave a sample mean weekly sale of x = $10,960. Does this indicate that the population mean weekly sales
is now more than $9820? Test at the 5% level of significance. Assume σ = $1580.
A. State the null and alternate hypotheses.
1. A. __________
(a) H0: µ = 9820; H1: µ < 9820
(b) H0: µ = 9820; H1: µ > 9820
(c) H0: x = 10,960; H1: x > 10,960
(d) H0: µ = 10,960; H1: µ > 10,960
(e) H0: µ > 9820; H1: µ = 9820
B. Compute the z or t value of the sample test statistic.
(a) z = 5.10
(b) z = 0.10
(c) t = 0.72
(d) z = −5.10
B. __________
(e) t = −0.10
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.236
(b) P-value = 0.460
(c) P-value < 0.0001
(d) P-value > 0.0001
(e) Cannot determine
D. Find the critical value(s).
D. __________
(a) z0 = 2.33
(b) z0 = 1.96
(c) t0 = −1.96
(d) z0 = 1.645
(e) t0 = −1.96
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
E. __________
(c) Cannot determine
(d) The population mean weekly sales is less than $9820.
(e) The population mean weekly sales is more than $10,960.
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Part III: Sample Tests, Chapter 9
141
CHAPTER 9, FORM C, PAGE 2
2. The average annual salary of employees at Wintertime Sports was $28,750 last year. This year the
company opened another store. Suppose a random sample of 18 employees gave an average annual salary
of x = $25,810 with sample standard deviation s = $4230. Use a 1% level of significance to test the claim
that the average annual salary for all employees is different from last year’s average salary. Assume
salaries are normally distributed.
A. State the null and alternate hypotheses.
2. A. __________
(a) H0: µ = 28,750; H1: µ < 28,750
(b) H0: µ = 25,810; H1: µ ≠ 25,810
(c) H0: µ1 =µ2; H1: µ1 ≠µ2
(d) H0: x = 25,810; H1: x ≠ 25,810
(e) H0: µ = 28,750; H1: µ ≠ 28,750
B. Compute the z or t value of the sample test statistic.
(a) t = −2.95
(b) z = −2.95
(c) t = −2.87
(d) z = −12.51
B. __________
(e) t = 2.95
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) Cannot determine
(b) 0.01 < P-value < 0.02
(c) P-value < 0.010
(d) P-value > 0.010
(e) P-value < 0.005
D. Find the critical value(s).
D. __________
(a) t0 = 2.58
(b) t0 = ±1.96
(c) t0 = ±2.567
(d) t0 = ±2.898
(e) z0 = −2.567
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
(c) Cannot determine
(d) The average salary is less than $25,810.
(e) The average salary is different from $10,960.
Copyright © Houghton Mifflin Company. All rights reserved.
E. __________
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CHAPTER 9, FORM C, PAGE 3
3. The owner of Prices Limited claims that 75% of all the items in the store are less than $5. Suppose that
you check a random sample of 146 items in the store and find that 105 have prices less than $5. Does this
indicate that the items in the store costing less than $5 is different from 75%? Use α = 0.01.
A. State the null and alternate hypotheses.
1. A. __________
(a) H0: p1 = p2; H1: p1 ≠ p2
(b) H0: p = 5; H1: p ≠ 5
(c) H0: p̂ = 0.75; H1: p̂ ≠ 0.75
(d) H0: p = 0.75; H1: p ≠ 0.75
(e) H0: p̂ = 0.72; H1: p̂ ≠ 0.72
B. Compute the z or t value of the sample test statistic.
(a) t = −0.86
(b) t = −0.73
(c) z = −0.73
(d) z = 0.86
B. __________
(e) z = −0.86
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.2327
(b) P-value = 0.0975
(c) P-value = 0.3898
(d) P-value = 0.1949
(e) P-value = 0.8051
D. Find the critical value(s).
D. __________
(a) z0 = ±2.58
(b) z0 = −2.33
(c) z0 = ±1.96
(d) t0 = −1.645
(e) t0 = ±2.58
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
E. __________
(c) Cannot determine
(d) The items in the store cost less than $5.
(e) The items in the store do not cost less than $5.
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Part III: Sample Tests, Chapter 9
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CHAPTER 9, FORM C, PAGE 4
4. A random sample of 257 dog owners was taken 10 years ago, and it was found that 146 owned more than
one dog (Sample 1). Recently, a random sample of 380 dog owners showed that 200 owned more than
one dog (Sample 2). Do these data indicate that the proportion of dog owners owning more than one dog
has decreased? Use a 5% level of significance.
A. State the null and alternate hypotheses.
4. A. __________
(a) H0: p̂1 = p̂2 ; H1: p̂1 > p̂2
(b) H0: p1 = p2; H1: p1 < p2
146
(d) H0: p1 = p2; H1: p1 ≠ p2
(c) H0: p1 =
257
= 0.57; H1: p1 < 0.57
(e) H0: p1 = p2; H1: p1 > p2
B. Compute the z or t value of the sample test statistic.
(a) z = 0.04
(b) z = 1.04
(c) z = 0.08
(d) t = −0.08
B. __________
(e) t = 1.04
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.8508
(b) P-value = 0.4681
(c) P-value = 0.2984
(d) P-value = 0.4840
(e) P-value = 0.1492
D. Find the critical value(s).
D. __________
(a) t0 = ±1.96
(b) z0 = 2.33
(c) t0 = −1.645
(d) z0 = 1.645
(e) z0 = ±1.96
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
(c) Cannot determine
(d) More people own dogs.
(e) Less people own dogs.
Copyright © Houghton Mifflin Company. All rights reserved.
E. __________
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5. Seven manufacturing companies agreed to implement a time management program in hopes of improving
productivity. The average times, in minutes, it took the companies to produce the same quantity and kind
of part are listed below. Does this information indicate the program decreased production time? Assume
normal population distributions. Use α = 0.05.
Company
Before program (1)
After program (2)
1
75
70
2
112
110
3
89
88
4
95
100
5
80
80
6
105
100
A. State the null and alternate hypotheses.
7
110
99
5. A. __________
(a) H0: µ1 = µ2; H1: µ1 > µ2
(b) H0: µd = 0; H1: µd ≠ 0
(c) H0: µ1 = µ2; H1: µ1 < µ2
(d) H0: µd = 0; H1: µd > 0
(e) H0: µ = 0; H1: µ < 0
B. Compute the z or t value of the sample test statistic.
(a) t = 0
(b) z = 0.36
(c) t = 1.44
(d) t = 0.36
B. __________
(e) z = −1.44
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.1498
(b) P-value = 0.10
(c) P-value = 0.0749
(d) P-value > 0.250
(e) Cannot determine
D. Find the critical value(s).
D. __________
(a) t0 = 2.447
(b) t0 = 1.782
(c) t0 = 1.895
(d) z0 = 1.645
(e) t0 = 1.943
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
E. __________
(c) Cannot determine
(d) All manufacturing companies should implement the program.
(e) Some manufacturing companies should implement the program.
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Part III: Sample Tests, Chapter 9
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CHAPTER 9, FORM C, PAGE 6
6. An independent rating service is trying to determine which of two film developing ships has quicker
service. Over a period of 12 randomly selected times, the average waiting period to develop a
24-exposure roll sold at Shop 1 is 58 minutes with standard deviation 3.5 minutes. The average waiting
period at Shop 2 to develop a 24-exposure roll over a period of 8 randomly selected times is 53 minutes
with standard deviation 4.9 minutes. Using a 1% level of significance, can we say there is a difference in
the average waiting time at Shop 1 and Shop 2?
A. State the null and alternate hypotheses.
6. A. __________
(a) H0: x1 = x2 ; H1: x1 ≠ x2
(b) H0: µ1 =µ2; H1: µ1 ≠ µ2
(c) H0: µ1 = µ2; H1: µ1 > µ2
(d) H0: µ = 58; H1: µ ≠ 58
(e) H0: µd > 0; H1: µd ≠ 0
B. Compute the z or t value of the sample test statistic.
(a) z = 2.67
(b) t = 2.49
(c) t0 = ±2.67
(d) z = 2.49
B. __________
(e) t = 2.67
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) 0.010 < P-value < 0.025
(b) 0.02 < P-value < 0.05
(c) Cannot determine
(d) 0.01 < P-value < 0.02
C. __________
(e) 0.005 < P-value < 0.010
D. Find the critical value(s).
D. __________
(a) t0 = ±2.878
(b) z0 = ±2.56
(c) z0 = ±1.96
(d) t0 = 2.552
(e) t0 = 2.878
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
(b) Reject H0
(c) Cannot determine
(d) It takes about an hour to develop film.
(e) Shop 1 takes longer than Shop 2.
Copyright © Houghton Mifflin Company. All rights reserved.
E. __________
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CHAPTER 9, FORM C, PAGE 7
7. The personnel manager of a large retail clothing store suspects a difference in the mean amount of break
time taken by workers during the weekday shifts compared to that of the weekend shifts. It is suspected
that the weekday workers take longer breaks on the average. A random sample of 46 weekday workers
had a mean x1 = 53 minutes of break time per 8-hour shift. A random sample of 40 weekend workers had a
mean x2 = 47 minutes. Previous studies show that σ1 = 7.3 minutes and σ 2 = 9.1 minutes. Test the
manager’s suspicion at the 5% level of significance.
A. State the null and alternate hypotheses.
7. A. __________
(a) H0: µ1 = µ2; H1: µ1 < µ2
(b) H0: µ1 = µ2; H1: µ1 > µ2
(c) H0: µ1 = µ2; H1: µ1 ≠ µ2
(d) H0: x1 = x2 ; H1: x1 > x2
(e) H0: µd = 0; H1: µd > 0
B. Compute the z or t value of the sample test statistic.
(a) t = 3.34
(b) t = 0.73
(c) z = 0.73
(d) z = 1.645
B. __________
(e) z = 3.34
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) Cannot determine
(b) P-value = 0.0495
(c) P-value = 0.0008
(d) P-value = 0.0004
(e) P-value = 0.2327
D. Find the critical value(s).
D. __________
(a) t0 = 1.645
(b) t0 = ±1.96
(c) z0 = 1.645
(d) z0 = 3.34
(e) z0 = 2.33
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
E. __________
(c) Cannot determine
(d) All weekend workers take shorter breaks.
(e) Some weekend workers take shorter breaks.
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Part III: Sample Tests, Chapter 9
147
CHAPTER 9, FORM C, PAGE 8
8. A machine in the lodge at a ski resort dispenses a hot chocolate drink. The average cup of hot chocolate is
supposed to contain 7.75 ounces. We may assume that x has a normal distribution with σ = 0.3 ounce. A
random sample of 16 cups of hot chocolate from this machine show the average content to be 7.62 ounces.
Do you think the machine is out of adjustment and the average amount of hot chocolate is less than it is
supped to be? Use a 5% level of significance.
A. State the null and alternate hypotheses.
8. A. __________
(a) H0: µ1 = µ2; H1: µ1 < µ2
(b) H0: µ = 7.75; H1: µ ≠ 7.75
(c) H0: x = 7.62; H1: x < 7.62
(d) H0: µ > 7.62; H1: µ = 7.62
(e) H0: µ = 7.75; H1: µ < 7.75
B. Compute the z or t value of the sample test statistic.
(a) t = −1.73
(b) z = −1.645
(c) z = −1.73
(d) t = −0.03
B. __________
(e) z = −0.03
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.0836
(b) P-value = 0.4880
(c) P-value = 0.4880
(d) P-value = 0.0418
(e) P-value = 0.9582
D. Find the critical value(s).
D. __________
(a) z0 = −1.645
(b) z0 = ±2.58
(c) z0 = ±1.96
(d) z0 = 1.645
(e) t0 = −1.645
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
(c) Cannot determine
(d) The cup will be over full.
(e) The machine is working fine.
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E. __________
148
Instructor’s Resource Guide Understandable Statistics, 8th Edition
CHAPTER 9, FORM C, PAGE 9
9. The average number of miles on vehicles traded in at Smith Brothers Motors is 64,000. Smith Brothers
Motors has started a new deal offering lower financing charges. They are interested in whether the
average mileage on trade-in vehicles has decreased. Test using α = 0.01 and the results (in thousands)
from a random sample printed below (taken after the deal started). Assume mileage is normally
distributed.
39
90
47
50
62
99
110
41
58
28
A. State the null and alternate hypotheses.
9. A. __________
(a) H0: x = 62, 400; H1: x ≠ 62,400
(b) H0: x = 64, 000; H1: x > 64,000
(c) H0: µd = 64,000; H1: µd < 64,000
(d) H0: µ = 64,000; H1: µ < 64,000
(e) H0: µ > 64,000; H1: µ > 64,000
B. Compute the z or t value of the sample test statistic.
(a) t = −0.52
(b) t = −0.18
(c) t = −0.17
(d) t = −0.02
B. __________
(e) z = −0.58
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) Cannot determine
(b) P-value = 0.4286
(c) P-value = 0.4325
(d) P-value > 0.250
(e) P-value > 0.125
D. Find the critical value(s).
D. __________
(a) t0 = 2.821
(b) z0 = −2.33
(c) t0 = −2.821
(d) t0 = −3.250
(e) t0 = −2.764
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
E. __________
(c) Cannot determine
(d) People are trading in more vehicles.
(e) People are trading in fewer vehicles.
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Part III: Sample Tests, Chapter 9
149
CHAPTER 9, FORM C, PAGE 10
10. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend
college after graduation. A random sample of 200 high school seniors from this city showed 162 plan to
attend college. Does this indicate that the percentage has increased from that of previous studies? Test at
5% level of significance.
A. State the null and alternate hypotheses.
10. A. __________
(a) H0: µ = 0.79; H1: µ > 0.79
(b) H0: p = 0.79; H1: p ≠ 0.79
(c) H0: p = 0.79; H1: p > 0.79
(d) H0: p̂ = 0.81; H1: p̂ ≠ 0.81
(e) H0: p̂ = 0.79; H1: p̂ > 0.79
B. Compute the z or t value of the sample test statistic.
(a) z = 0.72
(b) t = 1.645
(c) z = 0.62
(d) z = 1.645
B. __________
(e) z = 0.69
C. Find the P-value or an interval containing the P-value for the sample test
statistic.
(a) P-value = 0.2676
(b) P-value = 0.7642
(c) P-value > 0.05
(d) P-value = 0.2451
(e) P-value = 0.2358
D. Find the critical value(s).
D. __________
(a) z0 = 1.645
(b) t0 = 2.33
(c) z0 = 2.33
(d) t0 = ±2.58
(e) z0 = ±1.96
E. Based on your answers for parts A−D, what is your conclusion?
(a) Do not reject H0
C. __________
(b) Reject H0
(c) Cannot determine
(d) More seniors are going to college.
(e) Less seniors are going to college.
Copyright © Houghton Mifflin Company. All rights reserved.
E. __________