Lesson 10 – Homework 10
Notes:
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You may use Minitab when appropriate and include the Minitab output in your
homework. To place Minitab output into your homework, highlight the
portion of the Minitab printout you want, copy that to the clipboard, and
then paste it into the document.
Remember to check for the assumptions before you determine what procedure to
use. If there is no complete data, but only summary statistic, just mention what to
check.
Show your work to get full credit.
In this homework, one important issue is to identify whether to use 2-sample t-procedure
or to use paired t-procedure. See sample problems to make the distinction. In addition,
you should check whether to use pooled t or separate variances t if 2-sample t is
appropriate.
Homework problems (submit to Dropbox for HW 10 by its due day)
1. (15 pts; 5pts each) A firm has a generous but rather complicated policy concerning end
of the year bonuses for its lower level managerial personnel. The policy’s key factor is a
subjective judgment of “contributions to corporate goals”. A personnel officer took
samples of 27 female and 33 male managers to see whether there was any difference in
bonuses, expressed as a percentage of yearly salary. The data are listed here:
female
male
9.2
7.7
11.9
6.2
9
8.4
6.9
7.6
7.4
8
9.9
6.7
8.4
9.3
9.1
8.7
9.2
9.1
8.4
9.6
7.7
9
9
8.4
9.2
9.9
9
10.4
8.9
11.7
12
8.7
9.4
9.8
9
9.2
9.7
9.1
8.8
7.9
9.9
10
10.1
9
11.4
8.7
9.6
9.2
9.7
8.9
9.2
9.4
9.7
8.9
9.3
10.4
11.9
9
12
9.6
a) Use Minitab to find the value of the pooled variance t statistic (the usual t test based on
equal variance assumption).
b) Use Minitab to find the value of the t’ (separate variances t ) statistic.
c) Use both statistics to test the research hypothesis of unequal means at =.01 and at
=.001. (Use p-value from the Minitab output.) For this data set, does the conclusion
depend on which statistic is used?
2. (16 pts; 4pts each) A study was designed to measure the effect of learning environment
on academic achievement of 12 year-old students. Because genetic differences may also
contribute to academic achievement the researcher wanted to control for this factor.
Thirty sets of identical twins at age 12 were identified, with one twin placed in a class in
which academics were emphasized and the other twin placed in a class in which
academics were not emphasized. After one semester, the grades (based on 100 points) of
the 60 students were collected and shown here:
Academic
78
75
68
92
55
74
65
80
98
52
67
55
89
76
75
90
89
73
61
76
81
89
82
70
68
74
85
87
95
78
Non-Academic
71
70
66
85
60
72
57
75
92
56
63
52
84
67
74
88
80
65
60
74
76
78
78
62
73
73
75
88
94
75
Paired T-Test and CI: Academic, Non-Academic
Two-Sample T-Test and CI: Academic, Non-Academic
a) Use the Minitab output above to evaluate whether there is a difference in the mean
final grade between the students in an academically oriented learning environment and
those in a non-academically oriented environment.
b) Estimate the size of the difference in the mean final grades of the students in
academically and nonacademic learning environments. That is, provide a 95% confidence
interval for the difference.
c) Do the conditions for using the t procedures appear to be satisfied for these data?
d) Does it appear that using twins for this study to control for variation in final scores was
effective as compared to just taking a random sample of 30 students in both types of
home environments? Justify your answer.
3. (16 pts; 4pts each) In an environmental impact study for a new airport, the noise level
of various jets was measured just seconds after their wheels left the ground. The jets
were either wide-bodied or narrow-bodied. The noise levels in decibels (dB) are
recorded here for 15 wide-bodied jets and 12 narrow-bodied jets.
WideBodied
109
107
105
117
105
114
122
109
108
106
105
110
111
NarrowBodied
111
112
131
127
114
127
108
122
107
116
115
112
124
116
a) Do these two types of jets have different mean noise levels? Report the p-value of the
test statistic.
b) Estimate the size of the difference in mean noise level between the two types of jets
using a 98% confidence interval.
c) Use the confidence interval in b) to draw conclusion about whether the two types of
jets have different mean noise levels at =.02.
d) Is the difference of practical significance? Explain your point of view.
4. (15 pts; 5pts each) All persons running for public office must report the amount of
money spent during their campaign. Political scientists have contended that female
candidates generally find it difficult to raise money and therefore spend less in their
campaign than male candidates. Suppose the accompanying data represent the campaign
expenditures of a randomly selected group of male and female candidates for the state
legislature. Do the data support the claim that female candidates generally spend less in
their campaigns for public office than male candidates?
Female
Male
169
206
257
294
252
283
240
207
230
183
298
269
256
277
300
126
318
184
252
305
289
334
278
268
336
438
388
388
394
394
425
386
356
342
305
365
355
312
209
458
a) State the null and alternative hypotheses. Draw the appropriate graph in Minitab
to find out whether you can use t-procedure to analyze the data.
b) Perform the appropriate t procedure by Minitab. Draw a conclusion at =.02.
c) Estimate the size of difference in campaign expenditures for female and male
candidates by a 98% confidence interval. Hand compute the t-interval by formula
using mean values and standard deviations that are given by the results from the ttest.
5. (15 pts; 5 pts each) The costs of major surgery vary substantially from one state to
another due to differences in hospital fees, malpractice insurance cost, doctors’ fees and
rent. A study of hysterectomy costs was done in California and Montana. Based on a
random sample of 200 patient records from each state, the sample statistics shown here
were obtained.
State
n
Sample Mean
Montana
California
200
200
$7,458
$12,690
Sample Standard
Deviation
$320
$890
a) Is there significant evidence that California has a higher mean hysterectomy cost
than Montana? Can you use a two-sample t-test for this problem? Explain.
b) Estimate the difference in the mean costs of the two states using a 95%
confidence interval.
c) Justify your choice between using the pooled t-test and the separate variance t-test
in part (a).
6. (15 pts) Current Population Reports presents data on the ages of married people. Ten
married couples are randomly selected and have the ages shown here:
Husband
54
21
32
78
70
33
68
35
54
52
Wife
53
22
33
74
64
35
67
30
45
48
Do the data suggest that the mean age of married men is greater than the mean age of
married women? Perform the test at 5% significance level using both 2-sample t-test and
paired t-test. Do the two test results agree? Explain which test is more appropriate?
7. (8 pts) For the research question in the above problem, if we want to conduct a survey
so that we can have a power of 0.8 to detect a difference of one year at 2% level of
significance, how many married couples should we sample? You may use Minitab
“Power and sample size” to find the sample size. Use the data given in the above
problem to estimate for standard deviation. (Be careful about whether it is a one tailed or
two tailed alternative).