Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) The table shows the number of smokers in a random sample of 500 adults aged 20-24 and the
number of smokers in a random sample of 450 adults aged 25-29. Assume that you plan to use a
significance level of = 0.10 to test the claim that p1 p2 . Find the critical value(s) for this
1)
hypothesis test. Do the data provide sufficient evidence that the proportion of smokers in the 20-24
age group is different from the proportion of smokers in the 25-29 age group?
Number in sample
Number of smokers
Age 20-24
500
110
A) z = 1.28; no
Age 25-29
450
63
B) z = ± 1.645; yes
C) z = ± 1.96; no
D) z = ± 1.28; yes
Find sd.
2) Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the
nearest tenth.
A) 15.3
B) 16.2
C) 13.1
D) 15.7
Solve the problem.
3) The table shows the number satisfied in their work in a sample of working adults with a college
education and in a sample of working adults without a college education. Assume that you plan to
use a significance level of = 0.05 to test the claim that p1 > p2 . Find the critical value(s) for this
2)
3)
hypothesis test. Do the data provide sufficient evidence that a greater proportion of those with a
college education are satisfied in their work?
Number in sample
Number satisfied in their work
A) z = -1.645; yes
College Education
130
58
No College Education
123
50
B) z = 1.96; yes
C) z = 1.645; no
D) z = ± 1.96; no
4) When performing a hypothesis test for the ratio of two population variances, the upper critical F
value is denoted FR. The lower critical F value, FL, can be found as follows: interchange the
degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR
can be denoted F /2 and FL can be denoted F1- /2 .
Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:
n 1 = 10, n 2 = 16,
= 0.05
A) 0.2653, 3.7743
B) 0.3202, 3.1227
C) 3.1227, 3.7743
1
D) 0.2653, 3.1227
4)
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 .
5) A paint manufacturer wanted to compare the drying times of two different types of paint.
Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and
applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are
as follows.
Type A
Type B
5)
x1 = 71.5 hr x2 = 68.5 hr
s1 = 3.4 hr
s2 = 3.6 hr
n 1 = 11
n2 = 9
Construct a 99% confidence interval for µ1 - µ2 , the difference between the mean drying time for
paint type A and the mean drying time for paint type B.
A) -0.14 hrs < µ1 - µ2 < 6.14 hours
B) -1.00 hrs < µ1 - µ2 < 7.00 hrs
C) -1.51 hrs < µ1 - µ2 < 7.51 hrs
D) -2.24 hrs < µ1 - µ2 < 8.24 hrs
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.
6) A researcher was interested in comparing the amount of time spent watching television by women
6)
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 s2 = 5.2 hrs
n 1 = 14
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.
A) -6.05 hrs < µ1 - µ2 < 3.25 hrs
B) -6.04 hrs < µ1 - µ2 < 3.24 hrs
C) -5.92 hrs < µ1 - µ2 < 3.12 hrs
D) -5.91 hrs < µ1 - µ2 < 3.11 hrs
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is µd = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
7) x 9 6 7 5 12
y 6 8 3 6
7
A) t = 0.578
B) t = 2.890
Assume that you plan to use a significance level of
7)
C) t = 0.415
D) t = 1.292
= 0.05 to test the claim that p1 = p2 . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
8) A random sampling of sixty pitchers from the National League and fifty-two pitchers from the
American League showed that 19 National and 8 American League pitchers had E.R.A's below 3.5.
A) z = 2.009
B) z = 2.612
C) z = 272.163
D) z = 22.404
2
8)
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
n 2 = 50
9) n 1 = 50
x1 = 8
A) 0.6103
x2 = 7
B) 0.7794
9)
C) 0.2206
D) 0.3897
Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
10) The table below shows the weights of 9 subjects before and after following a particular diet for two
months.
Subject A
B
C
D
E
F
G
H
I
Before 168 180 157 132 202 124 190 210 171
After 162 178 145 125 171 126 180 195 163
Construct a 99% confidence interval for the mean difference of the "before" minus "after" weights.
A) -0.6 < µd < 20.4
B) 2.4 < µd < 17.4
C) 4.51 < µd < 15.7
D) 2.8 < µd < 17.0
Provide an appropriate response.
11) In the context of a hypothesis test for two proportions, which of the following statements about the
10)
11)
pooled sample proportion, p, is/are true?
I. It estimates the common value of p1 and p2 under the assumption of equal proportions.
^
^
II. It is obtained by averaging the two sample proportions p1 and p2 .
III. It is equal to the proportion of successes in both samples combined.
A) III only
B) I and II
C) I and III
D) I, II, and III
Solve the problem.
12) A manager at a bank is interested in the standard deviation of the waiting times when a single
waiting line is used and when individual lines are used. He wishes to test the claim that the
population standard deviation for waiting times when multiple lines are used is greater than the
population standard deviation for waiting times when a single line is used. Find the P-value for a
test of this claim given the following sample data. You won't be able to find the exact P-value, but
will be able to give a range of possible values.
12)
Sample 1: multiple waiting lines: n 1 = 13, s1 = 2.1 minutes
Sample 2: single waiting line: n 2 = 16, s2 = 1.1 minutes
A) 0.01 < P-value < 0.025
C) 0.02 < P-value < 0.05
B) 0.005 < P-value < 0.01
D) 0.025 < P-value < 0.05
Find the number of successes x suggested by the given statement.
13) Among 780 people selected randomly from among the residents of one city, 20.38% were found to
be living below the official poverty line.
A) 164
B) 159
C) 160
D) 158
3
13)
Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
14) A test of abstract reasoning is given to a random sample of students before and after they
completed a formal logic course. The results are given below. Construct a 95% confidence interval
for the mean difference between the before and after scores.
Before 74 83 75 88 84 63 93 84 91 77
After 73 77 70 77 74 67 95 83 84 75
A) 0.2 < µd < 7.2
B) 1.2 < µd < 5.7
Assume that you plan to use a significance level of
C) 1.0 < µd < 6.4
D) 0.8 < µd < 6.6
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the pooled estimate p. Round your answer to the nearest thousandth.
n 2 = 100
15) n 1 = 100
^
p1 = 0.11
14)
15)
^
p2 = 0.15
A) 0.361
B) 0.260
C) 0.130
D) 0.163
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.
16) x1 = 15, n1 = 50 and x2 = 23, n2 = 60; Construct a 90% confidence interval for the difference
between population proportions p1 - p2 .
A) 0.477 < p1 - p2 < 0.122
B) -0.232 < p1 - p2 < 0.065
C) 0.123 < p1 - p2 < 0.477
D) 0.151 < p1 - p2 < 0.449
4
16)
State what the given confidence interval suggests about the two population means.
17) A researcher was interested in comparing the heights of women in two different countries.
Independent simple random samples of 9 women from country A and 9 women from country B
yielded the following heights (in inches).
Country A Country B
65.3
64.1
60.2
66.4
61.7
61.7
65.8
62.0
61.0
67.3
64.6
64.9
60.0
64.7
65.4
68.0
59.0
63.6
The following 90% confidence interval was obtained for µ1 - µ2 , the difference between the mean
17)
height of women in country A and the mean height of women in country B.
-4.34 in. < µ1 - µ2 < -0.03 in
What does the confidence interval suggest about the population means?
A) The confidence interval includes only negative values which suggests that the two population
means might be equal. There doesn't appear to be a significant difference between the mean
height of women from country A and the mean height of women from country B.
B) The confidence interval includes only negative values which suggests that the mean height of
women from country A is greater than the mean height of women from country B.
C) The confidence interval includes 0 which suggests that the two population means might be
equal. There doesn't appear to be a significant difference between the mean height of women
from country A and the mean height of women from country B.
D) The confidence interval includes only negative values which suggests that the mean height of
women from country A is smaller than the mean height of women from country B.
Solve the problem.
18) Determine whether the following statement regarding the hypothesis test for two population
proportions is true or false:
18)
However small the difference between two population proportions, for sufficiently large sample
sizes, the null hypothesis of equal population proportions is likely to be rejected.
A) False
B) True
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
19) A report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were
burglarized and 23 out of 197 without pet dogs were burglarized.
A) z = -0.002
B) z = -0.459
C) z = -1.952
D) z = -1.148
The two data sets are dependent. Find d to the nearest tenth.
20) X 10.9 11.3 11.7 12.9 13.5
Y 11.0 12.6 12.4 10.7 11.2
A) 0.3
B) 0.5
19)
20)
C) 0.7
5
D) 0.6
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 .
21) 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
21)
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.
A) -7.41 hrs < µ1 - µ2 < 0.01 hrs
B) -7.25 hrs < µ1 - µ2 < -0.15 hrs
C) -7.13 hrs < µ1 - µ2 < -0.27 hrs
D) -6.55 hrs < µ1 - µ2 < -0.85 hrs
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.
22) x1 = 44, n1 = 64 and x2 = 50, n2 = 73; Construct a 95% confidence interval for the difference
between population proportions p1 - p2 .
A) 0.532 < p1 - p2 < 0.843
B) -0.153 < p1 - p2 < 0.158
C) 0.502 < p1 - p2 < 0.873
D) -0.183 < p1 - p2 < 0.873
23) 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) 0.0247 < p1 - p2 < 0.0286
B) -0.0177 < p1 - p2 < 0.1243
C) -0.0034 < p1 - p2 < 0.0566
22)
23)
D) -0.0443 < p1 - p2 < 0.0976
Solve the problem.
24) The 95% confidence interval for a collection of paired sample data is 0.0 < µd < 3.4. Based on the
24)
same sample, a traditional hypothesis test fails to support the claim of ud > 0. What can you
conclude about the significance level of the hypothesis test?
A) < 0.05
B) > 0.05
C) = 0.01
D)
= 0.05
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of
the test statistic that would result in rejection of the null hypothesis.
25) Suppose you wish to test the claim that µd, the mean value of the differences d for a population of
25)
paired data, is greater than 0. Given a sample of n = 15 and a significance level of
criterion would be used for rejecting the null hypothesis?
A) Reject null hypothesis if test statistic > 2.602.
B) Reject null hypothesis if test statistic > 2.977 or < -2.977.
C) Reject null hypothesis if test statistic < 2.624.
D) Reject null hypothesis if test statistic > 2.624.
6
= 0.01, what
Solve the problem.
26) When performing a hypothesis test for the ratio of two population variances, the upper critical F
value is denoted FR. The lower critical F value, FL, can be found as follows: interchange the
26)
degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR
can be denoted F /2 and FL can be denoted F1- /2 .
Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:
n 1 = 4, n 2 = 8,
= 0.05
A) 0.1211, 4.3541
B) 0.1112, 5.0453
C) 0.0684, 5.8898
D) 0.1703, 5.8898
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.
27) A researcher was interested in comparing the GPAs of students at two different colleges.
27)
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: x1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.)
A) -0.78 < µ1 - µ2 < 0.13
B) -0.75 < µ1 - µ2 < 0.10
D) -0.70 < µ1 - µ2 < 0.05
C) -0.81 < µ1 - µ2 < 0.15
7
28) A researcher was interested in comparing the heights of women in two different countries.
Independent simple random samples of 9 women from country A and 9 women from country B
yielded the following heights (in inches).
Country A Country B
64.1
65.3
66.4
60.2
61.7
61.7
62.0
65.8
67.3
61.0
64.9
64.6
64.7
60.0
68.0
65.4
63.6
59.0
Construct a 90% confidence interval for µ1 - µ2 , the difference between the mean height of women
28)
in country A and the mean height of women in country B.
(Note: x1 = 64.744 in., x2 = 62.556 in., s1 = 2.192 in., s2 = 2.697 in.)
A) 0.14 in. < µ1 - µ2 < 4.24 in.
B) 0.17 in. < µ1 - µ2 < 4.21 in.
C) 0.15 in. < µ1 - µ2 < 4.23 in.
D) 0.16 in. < µ1 - µ2 < 4.22 in.
Find the number of successes x suggested by the given statement.
29) Among 710 people selected randomly from among the eligible voters in one city, 60.6% were
homeowners.
A) 433
B) 427
C) 431
D) 430
29)
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 .
30) A researcher was interested in comparing the resting pulse rates of people who exercise regularly
and people who do not exercise regularly. Independent simple random samples were obtained of
16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse
rate (in beats per minute) of each person was recorded. The summary statistics are as follows.
Do Not Exercise
Do Exercise
30)
x1 = 72.5 beats/min x2 = 68.5 beats/min
s1 = 10.4 beats/min s2 = 8.9 beats/min
n 1 = 16
n 2 = 12
Construct a 90% confidence interval for the difference between the mean pulse rate of people who
do not exercise regularly and the mean pulse rate of people who exercise regularly.
A) -0.92 beats/min < µ1 - µ2 < 8.92 beats/min
B) -3.05 beats/min < µ1 - µ2 < 11.05 beats/min
C) -0.11 beats/min < µ1 - µ2 < 8.11 beats/min
D) -2.38 beats/min < µ1 - µ2 < 10.38 beats/min
The two data sets are dependent. Find d to the nearest tenth.
31) X 236 190 220 182 253 295 302
Y 194 153 195 153 235 253 284
A) 181.2
B) 18.1
31)
C) 39.3
8
D) 30.2
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
n 2 = 100
32) n 1 = 100
x1 = 38
A) 0.7718
x2 = 40
B) 0.0412
Assume that you plan to use a significance level of
C) 0.1610
32)
D) 0.2130
= 0.05 to test the claim that p1 = p2 . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
n 2 = 184
33) n 1 = 190
x1 = 78
A) z = 18.096
x2 = 69
B) z = 9.744
C) z = 0.399
33)
D) z = 0.703
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.
34) Independent samples from two different populations yield the following data. x1 = 958, x2 = 157,
34)
s1 = 77, s2 = 88. The sample size is 478 for both samples. Find the 85% confidence interval for
µ1 - µ2 .
A) 781 < µ1 - µ2 < 821
B) 800 < µ1 - µ2 < 802
C) 791 < µ1 - µ2 < 811
D) 794 < µ1 - µ2 < 808
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.
35) x1 = 59, n1 = 117 and x2 = 68, n2 = 119; Construct a 98% confidence interval for the difference
between population proportions p1 - p2 .
A) -0.218 < p1 - p2 < 0.084
B) 0.377 < p1 - p2 < 0.631
C) -0.194 < p1 - p2 < 0.631
D) 0.353 < p1 - p2 < 0.655
35)
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
36) In a vote on the Clean Water bill, 46% of the 205 Democrats voted for the bill while 48% of the 230
36)
Republicans voted for it.
A) z = -0.250
B) z = -0.417
C) z = -0.354
D) z = -0.459
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
n 2 = 140
37) n 1 = 100
x1 = 41
A) 0.0086
x2 = 35
B) 0.0512
C) 0.0021
37)
D) 0.4211
Determine whether the samples are independent or dependent.
38) 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) Dependent samples
B) Independent samples
9
38)
Solve the problem.
39) A hypothesis test is to be performed to test the equality of two population means. The sample sizes
are large and the samples are independent. A 95% confidence interval for the difference between
the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the
following do you know for sure:
39)
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A only
C) A and C
D) A, B, and C
Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
40) Ten different families are tested for the number of gallons of water a day they use before and after
viewing a conservation video. Construct a 90% confidence interval for the mean of the differences.
Before 33 33 38 33 35 35 40 40 40 31
After 34 28 25 28 35 33 31 28 35 33
A) 1.5 < µd < 8.1
B) 1.8 < µd < 7.8
C) 3.8 < µd < 5.8
40)
D) 2.5 < µd < 7.1
Solve the problem.
41) When performing a hypothesis test for the ratio of two population variances, the upper critical F
value is denoted FR. The lower critical F value, FL , can be found as follows: interchange the
41)
degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR can
be denoted F /2 and FL can be denoted F1- /2.
Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:
n 1 = 9, n 2 = 7,
= 0.05
A) 0.2150, 5.5996
B) 0.2411, 4.1468
C) 0.3931, 4.1468
The two data sets are dependent. Find d to the nearest tenth.
42) A 69 66 61 63 51
B 25 23 20 25 22
A) 39.0
B) 50.7
10
D) 0.2150, 4.8232
42)
C) 48.8
D) 23.4
Provide an appropriate response.
43) 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. A 95% confidence interval for the difference between the
proportion of 20-24 year olds and the proportion of 25-29 year olds who are smokers is
0.032 < p1 - p2 < 0.128.
43)
Which of the following statements give a correct interpretation of this confidence interval?
I. We can be 95% confident that the interval 0.032 to 0.128 contains the true difference between the
two population proportions.
II. There is a 95% chance that the true difference between the two population proportions lies
between 0.032 and 0.128.
III. If the process were repeated many times, each time selecting random samples of 500 people
aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for p1 p2 , 95% of the time the true difference between the two population proportions will lie between
0.032 and 0.128.
IV. If the process were repeated many times, each time selecting random samples of 500 people
aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for p1 p2 , 95% of the time the confidence interval limits will contain the true difference between the two
population proportions.
A) I and III
B) II and III
Assume that you plan to use a significance level of
C) II and IV
D) I and IV
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
n 2 = 75
44) n 1 = 50
x1 = 20
A) 0.0032
x2 = 15
B) 0.0001
C) 0.1201
44)
D) 0.0146
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.
45) Two types of flares are tested and their burning times are recorded. The summary statistics are
45)
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
Construct a 95% confidence interval for the differences between the mean burning time of the
brand X flare and the mean burning time of the brand Y flare.
A) 3.6 min < µX - µY < 5.0 min
B) 3.2 min < µX - µY < 5.4 min
C) 3.5 min < µX - µY < 5.1 min
D) 3.8 min < µX - µY < 4.8 min
11
46) A paint manufacturer wished to compare the drying times of two different types of paint.
Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and
applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are
as follows.
Type A
Type B
46)
x1 = 75.7 hrs x2 = 64.3 hrs
s1 = 4.5 hrs s2 = 5.1 hrs
n 1 = 11
n2 = 9
Construct a 98% confidence interval for µ1 - µ2 , the difference between the mean drying time for
paint of type A and the mean drying time for paint of type B.
A) 5.85 hrs < µ1 - µ2 < 16.95 hrs
B) 5.78 hrs < µ1 - µ2 < 17.02 hrs
C) 6.08 hrs < µ1 - µ2 < 16.72 hrs
D) 5.92 hrs < µ1 - µ2 < 16.88 hrs
Find the number of successes x suggested by the given statement.
47) Among 1350 randomly selected car drivers in one city, 8.74% said that they had been involved in
an accident during the past year.
A) 118
B) 116
C) 117
D) 119
Solve the problem.
48) The table shows the number of pitchers with E.R.A's below 3.5 in a random sample of sixty pitchers
from the National League and in a random sample of fifty-two pitchers from the American League.
Assume that you plan to use a significance level of = 0.05 to test the claim that p1 p2 . Find the
critical value(s) for this hypothesis test. Do the data support the claim that the proportion of
National League pitchers with an E.R.A. below 3.5 differs from the proportion of American League
pitchers with an E.R.A. below 3.5?
Number of pitchers in sample
Number of pitchers with E.R.A. below 3.5
A) z = 1.645; yes
National League
60
10
B) z = ± 2.575; no
American League
52
8
C) z = ± 1.645; yes
12
D) z = ± 1.96; no
47)
48)
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.
49) A researcher was interested in comparing the resting pulse rates of people who exercise regularly
49)
and the pulse rates of people who do not exercise regularly. She obtained independent simple
random samples of 16 people who do not exercise regularly and 12 people who do exercise
regularly. The resting pulse rates (in beats per minute) were recorded and the summary statistics
are as follows.
Do not exercise regularly
Exercise regularly
x1 = 72.9 beats/min
x2 = 69.4 beats/min
s1 = 10.9 beats/min
n 1 = 16
s2 = 8.2 beats/min
n 2 = 12
Construct a 95% confidence interval for µ1 - µ2 , the difference between the mean pulse rate of
people who do not exercise regularly and the mean pulse rate of people who exercise regularly.
A) -4.25 beats/min < µ1 - µ2 < 11.25 beats/min
B) -4.23 beats/min < µ1 - µ2 < 11.23 beats/min
C) -3.92 beats/min < µ1 - µ2 < 10.92 beats/min
D) -3.94 beats/min < µ1 - µ2 < 10.94 beats/min
Solve the problem.
50) A confidence interval estimate of the ratio
2
s1
2
s2
·
1
<
FR
2
1
2
2
<
2
s1
2
s2
·
2
1/
2
2 can be found using the following expression:
1
,
FL
where FR is found in the standard way and FL is found as follows: interchange the degrees of
freedom, and then take the reciprocal of the resulting F value found in table A-5.
A manager at a bank is interested in the standard deviation of the waiting times when a single
waiting line is used and when individual lines are used. Obtain a 95% confidence interval for
2
2 given the following sample data:
Sample 1: multiple waiting lines: n 1 = 13, s1 = 2.1 minutes
Sample 2: single waiting line: n 2 = 16, s2 = 0.8 minutes
A) 2.33 <
2
1/
2
2 < 21.91
B) 2.78 <
2
1/
2
2 < 18.05
C) 2.33 <
2
1/
2
2 < 20.4
D) 2.38 <
2
1/
2
2 < 17.43
13
2
1/
50)
51) The sample size needed to estimate the difference between two population proportions to within a
margin of error E with a confidence level of 1 - can be found as follows: in the expression
p1 q1 p2 q2
+
E = z /2
n1
n2
51)
replace n 1 and n 2 by n (assuming both samples have the same size) and replace each of p1 , q1 , p2 ,
and q2 by 0.5 (because their values are not known). Then solve for n.
Use this approach to find the size of each sample if you want to estimate the difference between the
proportions of men and women who plan to vote in the next presidential election. Assume that
you want 99% confidence that your error is no more than 0.02.
A) 4803
B) 8289
C) 3220
D) 6787
Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
52) If d = 3.125, Sd = 2.911, and n = 8, determine a 95 percent confidence interval for µd.
A) 0.691 < µd < 5.559
52)
B) 0.691 < µd < 3.986
D) 2.264 < µd < 5.559
C) 2.264 < µd < 3.986
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 .
53) 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 the difference between the mean GPA of college A students
and the mean GPA of college B students.
53)
(Note: x1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.)
A) -0.91 < µ1 - µ2 < 0.25
B) -0.65 < µ1 - µ2 < -0.01
C) -0.81 < µ1 - µ2 < 0.15
D) -0.72 < µ1 - µ2 < 0.07
Find the number of successes x suggested by the given statement.
54) A computer manufacturer randomly selects 2680 of its computers for quality assurance and finds
that 1.98% of these computers are found to be defective.
A) 56
B) 53
C) 51
D) 58
14
54)
Determine whether the samples are independent or dependent.
55) The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample
with decaffeinated soda.
A) Independent samples
B) Dependent samples
55)
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is µd = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
56) The following table shows the weights of nine subjects before and after following a particular diet
for two months. You wish to test the claim that the diet is effective in helping people lose weight.
What is the value of the appropriate test statistic?
Subject A
B
C
D
E
F
G
H
I
Before 168 180 157 132 202 124 190 210 171
After 162 178 145 125 171 126 180 195 163
A) 0.351
B) 3.156
C) 1.052
D) 9.468
Solve the problem.
57) When performing a hypothesis test for the ratio of two population variances, the upper critical F
value is denoted FR. The lower critical F value, FL, can be found as follows: interchange the
56)
57)
degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR
can be denoted F /2 and FL can be denoted F1- /2 .
Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:
n 1 = 25, n 2 = 16,
= 0.10
A) 0.7351, 2.2378
B) 0.4745, 2.4371
C) 0.4745, 2.2878
D) 0.5327, 2.2878
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.
58) A researcher was interested in comparing the salaries of female and male employees at a particular
58)
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
Construct a 98% confidence interval for µ1 - µ2, the difference between the mean weekly salary of
female employees and the mean weekly salary of male employees at the company.
(Note: x1 = $705.38, x2 = $817.07, s1 = $183.86, s2 = $330.15.)
A) -$382 < µ1 - µ2 < $158
B) -$385 < µ1 - µ2 < $164
C) -$431 < µ1 - µ2 < $208
D) -$383 < µ1 - µ2 < $159
15
Assume that you plan to use a significance level of
= 0.05 to test the claim that p1 = p2 , Use the given sample sizes and
numbers of successes to find the pooled estimate p. Round your answer to the nearest thousandth.
n 2 = 270
59) n 1 = 255
x1 = 82
A) 0.227
x2 = 88
B) 0.324
C) 0.292
59)
D) 0.162
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.
60) 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 .
A) 0.048 < p1 - p2 < 0.112
B) 0.025 < p1 - p2 < 0.135
C) 0.032 < p1 - p2 < 0.128
D) 0.035 < p1 - p2 < 0.125
16
60)
Answer Key
Testname: TEST 3
1) B
2) A
3) C
4) D
5) C
6) D
7) D
8) A
9) B
10) A
11) C
12) A
13) B
14) A
15) C
16) B
17) D
18) B
19) D
20) B
21) C
22) B
23) D
24) A
25) D
26) C
27) A
28) D
29) D
30) D
31) D
32) A
33) D
34) C
35) A
36) B
37) A
38) B
39) A
40) B
41) A
42) A
43) D
44) D
45) D
46) B
47) A
48) D
49) C
50) A
17
Answer Key
Testname: TEST 3
51) B
52) A
53) C
54) B
55) A
56) B
57) C
58) A
59) B
60) C
18