Chapter 10 Samples Were Selected From Three Populations The

Document Type
Test Prep
Book Title
Essentials of Modern Business Statistics 4th (Fourth) Edition By Williams 4th Edition
Authors
J.K
68. MNM, Inc. has three stores located in three different areas. Random samples of the daily
sales of the three stores (in $1,000) are shown below.
Store 1
Store 2
Store 3
9
10
6
8
11
7
7
10
8
8
13
11
At 95% confidence, test to see if there is a significant difference in the average sales of
the three stores. Show the complete ANOVA table.
69. Ten observations were selected from each of 3 populations, and an analysis of variance
was performed on the data. The following are the results.
ANOVA
Source of Variation
df
F
Between Groups
?
?
Within Groups
?
Total
?
At 95% confidence, test to see if there is a significant difference among the means of the
three populations.
70. The following are the results from a completely randomized design consisting of 3
treatments.
ANOVA
Source of Variation
df
F
Between Groups
?
?
Within Groups
?
Total
23
Using = .05, test to see if there is a significant difference among the means of the three
populations.
71. Eight observations were selected from each of 3 populations (total of 24 observations),
and an analysis of variance was performed on the data. The following are part of the
results.
ANOVA
Source of Variation
df
F
Between Groups
?
?
Within Groups
?
Total
?
Using = .05, test to see if there is a significant difference among the means of the three
populations.
72. Random samples of individuals from three different cities were asked how much time
they spend per day watching television. The results (in minutes) for the three groups are
shown below.
City I
City II
City III
260
182
211
280
190
190
240
220
247
260
240
300
a. Compute the overall sample mean
x
.
b. At = 0.05, test to see if there is a significant difference in the averages of the three
groups. Show the complete ANOVA table.
73. Three different brands of tires were compared for wear characteristics. From each brand
of tire, ten tires were randomly selected and subjected to standard wear-testing
procedures. The average mileage obtained for each brand of tire and sample variances
(both in 1,000 miles) are shown below.
Brand A
Brand C
Average Mileage
37
33
Sample variance
3
2
At 95% confidence, test to see if there is a significant difference in the average mileage
of the three brands.
74. MOA, Inc. has three stores located in three different areas. Random samples of the sales
of the three stores (In $1,000) are shown below.
Store 1
Store 2
Store 3
46
34
33
47
36
31
45
35
35
42
39
45
a. Compute the overall sample mean
x
.
b. At 95% confidence, test to see if there is a significant difference in the average sales
of the three stores. Show the complete ANOVA table.
75. In a completely randomized experimental design, 11 experimental units were used for
each of the 4 treatments. Part of the ANOVA table is shown below.
ANOVA
Source of Variation
df
F
Between Groups
?
?
Within Groups
?
Total
?
a. Determine all the missing values in the above table and fill in the blanks.
b. Use = 0.05 to determine if there is any significant difference among the means of
the four treatments.
76. Samples were selected from three populations. The data obtained are shown below.
Sample 1
Sample 2
Sample 3
10
16
15
9
14
15
12
13
16
13
14
14
16
10
17
Sample Mean (
j
x
)
11
15
14
Sample Variance (
2
j
s
)
3.33
2.4
5.5
a. Compute the overall sample mean
x
.
b. Set up an ANOVA table for this problem.
c. At 95% confidence test to determine whether there is a significant difference in the
means of the three populations.
77. In a completely randomized experimental design, 16 experimental units were used for
each of the 4 levels of the factor (i.e., 4 treatments). Part of the ANOVA table is shown
below.
ANOVA
Source of Variation
df
F
Between Groups
?
?
Within Groups
?
Total
?
a. Determine all the missing values in the above table and fill in the blanks.
b. Use = 0.05 to determine if there is any significant difference among the means of
the four groups.
78. Independent random samples of Company W employees were taken to compare salaries
between college graduates and high school graduates. Samples of size 30 were taken for
each group. The results follow.
Salary HS ($1000)
Salary College ($1000)
24.1
22.9
24.0
32.4
33.1
26.2
21.2
19.9
23.9
30.9
29.6
28.7
25.7
19.5
29.0
39.2
32.1
31.8
28.8
22.1
24.7
29.6
30.4
28.5
28.6
22.7
24.4
35.5
30.4
32.7
30.2
18.6
23.5
32.0
31.3
28.6
18.4
23.3
30.9
32.0
33.3
33.5
24.3
23.8
27.6
28.3
37.5
41.4
28.3
25.4
32.1
30.8
35.4
28.4
21.7
23.9
23.0
31.2
37.2
27.2
Use Excel to estimate the difference in average salaries between the two groups with a
95% level of confidence.
79. At a particular airport in the United States, independent samples of domestic flights from
two airlines were taken and the amount of time each flight was delayed was measured. The
results follow.
Minutes Delayed
Airline A
Minutes Delayed
Airline B
0.0
33.7
0.0
7.2
25.6
31.8
0.0
34.6
38.9
36.2
0.0
41.6
27.3
24.7
34.8
43.1
44.5
0.0
38.9
39.4
41.8
41.5
42.1
7.8
35.3
23.5
39.5
12.8
34.5
38.1
35.7
33.0
29.0
32.9
41.3
31.8
Use Excel to estimate the difference in average delay time between the two airlines with
a 95% level of confidence.
80. Independent samples of commuters are taken from two cities. The following data
represents the time (in minutes) to drive to work. Use Excel to determine whether the
average commuting times are significantly different between the two cities. Use = .05.
City A
City B
15.25
40.25
12.75
48.75
25.50
50.00
12.50
12.25
18.75
45.00
15.50
10.00
60.25
16.75
22.75
42.00
10.50
18.75
38.75
42.50
10.50
28.50
45.00
12.25
35.75
30.00
81. The following independent samples show the delivery times for two suppliers of raw
materials (in days). A company currently uses Supplier A but will switch to Supplier B if
its average delivery time is less than that for Supplier A. Use Excel to conduct the
appropriate hypothesis test. Use = .10.
Supplier A
Supplier B
10
12
3
6
13
13
15
4
12
14
7
6
14
10
2
4
14
8
18
16
12
8
20
18
10
12
9
4
5
8
82. Starting annual salaries for business school graduates majoring in finance and
management information systems (MIS) were collected in two independent random
samples. Use the following data to develop a 95% confidence interval estimate of the
difference between the starting salaries for the two majors. Based on previous studies,
the population standard deviations for Finance and MIS salaries are estimated to be
$2,100 and $2,600, respectively.
Finance
MIS
n1 = 60
n2 = 50
1
x
= $43,200
2
x
= $46,500
EMBS4-TB10.doc - 64
83. A manager is thinking of providing, on a regular basis, in-house training for employees
preparing for an inventory management certification exam. In the past, some employees
received the in-house training before taking the exam, while others did not. Independent
random samples taken from the company’s records provided the following exam scores
for 10 workers who did not receive in-house training and 8 workers who did receive
training. (The manager is confident that the distributions of both populations’ exam
scores are approximately normal.)
No Training
76
80
60
91
73
77
82
68
75
86
a. Develop a 95% confidence interval estimate for the difference between the
average test scores for the two populations of employees.
b. Using
= .05, test for any difference between the average test scores for the two
populations of employees.
84. A survey was recently conducted to determine if consumers spend more on computer-
related purchases via the Internet or store visits. Assume a sample of 8 respondents
provided the following data on their computer-related purchases during a 30-day period.
Using a .05 level of significance, can we conclude that consumers spend more on
computer-related purchases by way of the Internet than by visiting stores?
Expenditures (dollars)
Respondent
In-Store
Internet
1
132
225
2
90
24
3
119
95
4
16
55
5
85
13
6
248
105
7
64
57
8
49
0
85. Regional Manager Sue Collins would like to know if the mean number of telephone calls
made per 8-hour shift is the same for the telemarketers at her three call centers (Austin,
Las Vegas, and Albuquerque). A simple random sample of 6 telemarketers from each of
the three call centers was taken and the number of telephone calls made in eight hours by
each observed employee is shown below.
Observation
Center 1
Austin
Center 2
Las Vegas
Center 3
Albuquerque
1
82
72
71
2
68
63
81
3
77
74
73
4
80
60
68
5
69
70
76
6
78
73
80
Sample Mean
75.667
68.667
74.833
Sample Variance
33.867
33.467
26.167
Using
= .10, test for any significant difference in the mean number of telephone calls
made at the three call centers.

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