MATH 227
CP 10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have
been randomly selected
1) A researcher finds that of 1000 people who said that they attend a religious service at least
1)
once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who
had not attended a religious service at least once a month, 22 stopped to help a person with
car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.
2) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of
450 people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in
the two age groups is the same. Use a significance level of 0.01.
2)
3) Seven of 8500 people vaccinated against a certain disease later developed the disease. 18 of
10,000 people vaccinated with a placebo later developed the disease. Test the claim that the
vaccine is effective in lowering the incidence of the disease. Use a significance level of 0.02.
3)
Construct the indicated confidence interval for the difference between population proportions p1 - p2 . Assume that the
samples are independent and that they have been randomly selected.
4) x1 = 44, n1 = 64 and x2 = 50, n2 = 73; Construct a 95% confidence interval for the difference
4)
5) x1 = 59, n1 = 117 and x2 = 68, n2 = 119; Construct a 98% confidence interval for the
5)
6) In a random sample of 300 women, 45% favored stricter gun control legislation. In a
random sample of 200 men, 25% favored stricter gun control legislation. Construct a 98%
confidence interval for the difference between the population proportions p1 - p2 .
6)
7) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of
450 people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the
difference between the population proportions p1 - p2 .
7)
between population proportions p1 - p2 .
difference between population proportions p1 - p2 .
Test the indicated claim about the means of two populations. Assume that the two samples are independent simple
random samples selected from normally distributed populations. Do not assume that the population standard deviations
are equal. Use the traditional method or P-value method as indicated.
8) A researcher wishes to determine whether people with high blood pressure can reduce
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their blood pressure, measured in mm Hg, by following a particular diet. Use a
significance level of 0.01 to test the claim that the treatment group is from a population
with a smaller mean than the control group. Use the traditional method of hypothesis
testing.
Treatment Group
Control Group
n 1 = 35
n 2 = 28
x1 = 189.1
x2 = 203.7
s1 = 38.7
s2 = 39.2
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9) A researcher was interested in comparing the salaries of female and male employees at a
particular company. Independent simple random samples of 8 female employees and 15
male employees yielded the following weekly salaries (in dollars).
Female Male
495
722 518
760
562 904
556
880 1150
904
520 805
520
500 480
1005
1250 970
743
750 605
660
1640
Use a 0.05 significance level to test the claim that the mean salary of female employees is
less than the mean salary of male employees. Use the traditional method of hypothesis
testing.
9)
(Note: x 1 = $705.375, x2 = $817.067, s1 = $183.855, s2 = $330.146.)
Construct the indicated confidence interval for the difference between the two population means. Assume that the two
samples are independent simple random samples selected from normally distributed populations. Do not assume that the
population standard deviations are equal.
10) A researcher was interested in comparing the amount of time spent watching television by
10)
women and by men. Independent simple random samples of 14 women and 17 men were
selected, and each person was asked how many hours he or she had watched television
during the previous week. The summary statistics are as follows.
Women
Men
x1 = 12.6 hrs x2 = 14.0 hrs
s1 = 3.9 hrs
n 1 = 14
s2 = 5.2 hrs
n 2 = 17
Construct a 99% confidence interval for µ1 - µ2 , the difference between the mean amount
of time spent watching television for women and the mean amount of time spent watching
television for men.
11) A researcher was interested in comparing the GPAs of students at two different colleges.
Independent simple random samples of 8 students from college A and 13 students from
college B yielded the following GPAs.
College A College B
3.7
3.8
2.8
3.2
3.2
4.0
3.0
3.0
3.6
2.5
3.9
2.6
2.7
3.8
4.0
3.6
2.5
3.6
2.8
3.9
3.4
Construct a 95% confidence interval for µ1 - µ2 , the difference between the mean GPA of
college A students and the mean GPA of college B students.
(Note: x 1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.)
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11)
Perform the indicated hypothesis test. Assume that the two samples are independent simple random samples selected
from normally distributed populations. Also assume that the population standard deviations are equal ( 1 = 2 ), so that
the standard error of the difference between means is obtained by pooling the sample variances .
12) A researcher was interested in comparing the amount of time spent watching television by
women and by men. Independent simple random samples of 14 women and 17 men were
selected, and each person was asked how many hours he or she had watched television
during the previous week. The summary statistics are as follows.
Women
Men
12)
x1 = 11.4 hr x2 = 16.8 hr
s1 = 4.1 hr s2 = 4.7 hr
n 1 = 14
n 2 = 17
Use a 0.05 significance level to test the claim that the mean amount of time spent watching
television by women is smaller than the mean amount of time spent watching television by
men. Use the traditional method of hypothesis testing.
13) A researcher wishes to determine whether the blood pressure of vegetarians is, on average,
lower than the blood pressure of nonvegetarians. Independent simple random samples of
85 vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic
blood pressure:
Vegetarians
13)
Nonvegetarians
n 1 = 85
n 2 = 75
x1 = 124.1 mmHg
x2 = 138.7 mmHg
s1 = 38.7 mmHg
s2 = 39.2 mmHg
Use a significance level of 0.01 to test the claim that the mean systolic blood pressure for
vegetarians is lower than the mean systolic blood pressure for nonvegetarians. Use the
P-value method of hypothesis testing.
Construct the indicated confidence interval for the difference between the two population means. Assume that the two
samples are independent simple random samples selected from normally distributed populations. Also assume that the
population standard deviations are equal ( 1 = 2 ), so that the standard error of the difference between means is
obtained by pooling the sample variances .
14) A researcher was interested in comparing the amount of time spent watching television by
women and by men. Independent simple random samples of 14 women and 17 men were
selected and each person was asked how many hours he or she had watched television
during the previous week. The summary statistics are as follows.
Women
Men
x1 = 12.7 hr
s1 = 4.3 hr
n 1 = 14
x2 = 16.4 hr
s2 = 4.9 hr
n2 = 17
Construct a 95% confidence interval for µ1 - µ2 , the difference between the mean amount
of time spent watching television for women and the mean amount of time spent watching
television for men.
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14)
Answer Key
Testname: MATH227CP10
1) H0 : p1 = p2 .
H1 : p1
p2 .
Test statistic: z = 1.93. Critical values: z = ±1.96.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two
proportions are equal.
H1 : p1 p2 .
2) H0 : p1 = p2 .
Test statistic: z = 3.19.
Critical values: z = ±2.575.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of smokers
in the two age groups is the same.
H1 : p1 < p2 .
3) H0 : p1 = p2 .
Test statistic: z = -1.80.
Critical value: z = -2.05.
Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the vaccine is effective in
lowering the incidence of the disease.
4) -0.153 < p1 - p2 < 0.158
5) -0.218 < p1 - p2 < 0.084
6) 0.102 < p1 - p2 < 0.298
7) 0.032 < p1 - p2 < 0.128
8) H0 : µ1 = µ2 .
H1 : µ1 < µ2 .
Test statistic: t = -1.477.
Critical value: -2.473.
Do not reject the null hypothesis. There is not sufficient evidence to support the claim that the treatment group is from
a population with a smaller mean than the control group.
9) H0 : µ1 = µ2
H1 : µ1 < µ2
Test statistic: t = -1.042
Critical value: t = -1.725
Do not reject H0 . At the 5% significance level, there is not sufficient evidence to support the claim that the mean salary
of female employees is less than the mean salary of male employees.
10) -5.91 hrs < µ1 - µ2 < 3.11 hrs
11) -0.78 < µ1 - µ2 < 0.13
12) H0 : µ1 = µ2
H1 : µ1 < µ2
Test statistic: t = -3.369
Critical value: t = -1.699
Reject H0. At the 5% significance level, there is sufficient evidence to support the claim that the mean amount of time
spent watching television by women is smaller than the mean amount of time spent watching television by men.
13) H0 : µ1 = µ2
H1 : µ1 < µ2
Test statistic: t = -2.367
0.005 < P-value < 0.01
Reject H0. At the 1% significance level, there is sufficient evidence to support the claim that the mean systolic blood
pressure for vegetarians is lower than the mean systolic blood pressure for nonvegetarians.
14) -7.13 hrs < µ1 - µ2 < -0.27 hrs
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