chapter 9 practice - faculty.piercecollege.edu

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chapter 9 practice - faculty.piercecollege.edu
Math 227 / Fall 2014
Instructor: David Soto
Name______________________________________________
Chapter 2
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 marketing survey involves product recognition in New York and California. Of 558
1)
New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the
product. At the 0.05 significance level, test the claim that the recognition rates are the
same in both states.
2) Use the given sample data to test the claim that p1 < p2 . Use a significance level of 0.10.
Sample 1
Sample 2
n 1 = 462
n 2 = 380
x1 = 84
2)
x2 = 95
3) A researcher finds that of 1000 people who said that they attend a religious service at least
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4) In a random sample of 360 women, 65% favored stricter gun control laws. In a random
4)
5) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of
5)
6) Seven of 8500 people vaccinated against a certain disease later developed the disease. 18
6)
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.
sample of 220 men, 60% favored stricter gun control laws. Test the claim that the
proportion of women favoring stricter gun control is higher than the proportion of men
favoring stricter gun control. Use a significance level of 0.05.
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.
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.
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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.
7) A marketing survey involves product recognition in New York and California. Of 558 New
Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product.
Construct a 99% confidence interval for the difference between the two population proportions.
A) -0.0177 < p1 - p2 < 0.1243
B) -0.0034 < p1 - p2 < 0.0566
C) 0.0247 < p1 - p2 < 0.0286
7)
D) -0.0443 < p1 - p2 < 0.0976
8) In a random sample of 300 women, 45% favored stricter gun control legislation. In a random
8)
sample of 200 men, 25% favored stricter gun control legislation. Construct a 98% confidence
interval for the difference between the population proportions p1 - p2 .
A) 0.102 < p1 - p2 < 0.298
C) 0.092 < p1 - p2 < 0.308
B) 0.118 < p1 - p2 < 0.282
D) 0.114 < p1 - p2 < 0.286
Determine whether the samples are independent or dependent.
9) The effectiveness of a new headache medicine is tested by measuring the amount of time before
the headache is cured for patients who use the medicine and another group of patients who use a
placebo drug.
A) Independent samples
B) Dependent samples
9)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
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.
10) Two types of flares are tested and their burning times (in minutes) are recorded. The
10)
summary statistics are given below.
Brand X
Brand Y
n = 35
n = 40
x = 19.4 min
s = 1.4 min
x = 15.1 min
s = 0.8 min
Use a 0.05 significance level to test the claim that the two samples are from populations
with the same mean. Use the traditional method of hypothesis testing.
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11) A researcher was interested in comparing the GPAs of students at two different colleges.
11)
Independent 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
Use a 0.10 significance level to test the claim that the mean GPA of students at college A is
different from the mean GPA of students at college B. Use the P-value method of
hypothesis testing.
(Note: x1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.)
12) A researcher wishes to determine whether people with high blood pressure can reduce
12)
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
x 1 = 189.1
s1 = 38.7
x2 = 203.7
s2 = 39.2
13) A researcher was interested in comparing the amount of time (in hours) 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 = 12.5 hr
s1 = 3.9 hr
n 1 = 14
x2 = 13.8 hr
s2 = 5.2 hr
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.
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13)
14) A researcher was interested in comparing the resting pulse rates of people who exercise
14)
regularly and of those who do not exercise regularly. Independent simple random
samples of 16 people who do not exercise regularly and 12 people who exercise regularly
were selected, and the resting pulse rates (in beats per minute) were recorded. The
summary statistics are as follows.
Do not exercise regularly Exercise regularly
x1 = 73.0 beats/min
s1 = 10.9 beats/min
n 1 = 16
x2 = 68.4 beats/min
s2 = 8.2 beats/min
n 2 = 12
Use a 0.025 significance level to test the claim that the mean resting pulse rate of people
who do not exercise regularly is larger than the mean resting pulse rate of people who
exercise regularly. Use the traditional method of hypothesis testing.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the samples are independent or dependent.
15) The effectiveness of a headache medicine is tested by measuring the intensity of a headache in
patients before and after drug treatment. The data consist of before and after intensities for each
patient.
A) Dependent samples
B) Independent samples
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15)
Answer Key
Testname: CHAPTER 9 PRACTICE
1) H0 : p1 = p2 .
H1 : p1
p2 .
Test statistic: z = 0.97.
Critical values: z = ±1.96.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the recognition
rates are the same in both states.
H1 : p1 < p2 .
2) H0 : p1 = p2 .
Test statistic: z = -2.41.
Critical value: z = -1.28.
Reject the null hypothesis. There is sufficient evidence to support the claim that p1 < p2 .
3) 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 .
4) H0 : p1 = p2 .
Test statistic: z = 1.21. Critical value: z = 1.645.
Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of women
favoring stricter gun control is higher than the proportion of men favoring stricter gun control.
H1 : p1 p2 .
5) 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 .
6) 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.
7)
D
A
9) A
8)
10) H0 : µ1 = µ2 .
H1 : µ1
µ2 .
Test statistic t = 16.025.
Critical values: t = ±2.032.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from
populations with the same mean.
11) H0 : µ1 = µ2
H1 : µ1
µ2
Test statistic: t = -1.506
0.1 < P-value < 0.2
Do not reject H . At the 10% significance level, there is not sufficient evidence to support the claim that the mean
0
GPA of students at college A is different from the mean GPA of students at college B.
12) 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.
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Answer Key
Testname: CHAPTER 9 PRACTICE
13) H0 : µ1 = µ2
H1 : µ1 < µ2
Test statistic: t = -0.795
Critical value: t = -1.701
Do not reject H0 . At the 5% significance level, there is not 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.
14) H0 : µ1 = µ2
H1 : µ1 > µ2
Test statistic: t = 1.274
Critical value: t = 2.060
Do not reject H0 . At the 2.5% significance level, there is not sufficient evidence to support the claim that the mean
resting pulse rate of people who do not exercise regularly is larger than the mean resting pulse rate of people who
exercise regularly.
15) A
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