Chapter 9 Test B
Name: __________________________ Date: _____________
1. Find p and q , if x1  23, n1  43, x2  29, and n2  52 .
2. Donaldson Corporation wants to hire a temporary secretary. There are two employment
agencies in town, and it is believed that the average hourly wage charged by both
agencies are the same. Test this claim at   0.05 .
Agency A
Agency B
$6.25
$6.55
x
$0.40
$0.58
s
18
20
n
3. A conservationist wants to know if the average water level in Horseshoe Lake is more
than the average water level in Swan Lake. Test his hypothesis at   0.01 .
Horseshoe Lake
Swan Lake
43
38
x

3.2
2.4
23
23
n
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Chapter 9 Test B
4. Joan moves into her new apartment and wants to purchase a new couch. She wants to
determine if there is any difference between the average costs of couches at two
different stores. Test the hypothesis that there is no difference at   0.05 .
Store 1
Store 2
$650
$730
x

$61
$78
24
21
n
5. A local charity thinks that people in River Heights give more money to their charity
than people in Lakeview. They conducted a survey of 24 people in each subdivision
and recorded the results. Is their hypothesis correct? Let   0.01 .
River Heights
Lakeview
$35
$25
x
$5
$8
s
24
24
n
6. For the samples summarized below, test the hypothesis at α =.05 that the two variances
are equal.
Variance
Number of data values
Sample 1
24
10
Sample 2
9
20
7. Find p and q when X 1 =16, n1 =50, X 2 =25, and n 2 =80
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Chapter 9 Test B
8. In comparing the two variances below, what is the test value and what are the degrees of
freedom that should be used?
Variance
Number of values
Sample 1
7
12
Sample 2
10
26
9. A running coach wanted to see whether runners ran faster after eating spaghetti the night
before. 16 random runners were chosen for this study. They ran a 5 kilometer race after
having a normal dinner the night before, and then a week later, reran the same race after
having a spaghetti dinner the night before. Their results (in seconds) are in the table
below. At α = .01, what is the test value to use for this test?
Regular Dinner
Spaghetti
Difference
Dinner
by runner
Sample mean
1100
1090
–10
Sample variance
2400
2800
500
10. A college class believes that the average grade average of psychology students and the
average grade averages of biology students are different. The class found that the actual
grade averages of a sample of 11 psychology students was 3.5 and the average grade
average of a sample of 14 biology students was 3.5. What is the null hypothesis for this
study?
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Chapter 9 Test B
11. A dietician investigated whether apples washed in hot water or in cold water turned
brown at different rates when exposed to air. She took 10 random apples and cut each in
half. She washed one half of each apple in hot water and the other half in cold water,
and then put both halves out in a tray. Her results (in hours until turning a particular
shade of brown) are in the table below. At α = .01, did she see a difference between the
two treatments?
Hot Water
Cold Water
Difference
by apple
Sample mean
6.00
5.15
–0.85
Sample variance
2.10
2.00
0.55
12. 68% of students at a university live on campus. A random sample found that 25 of 45
male students and 39 of 50 of female students lived on campus. At the .05 level of
significance, is there sufficient evidence to conclude that a difference exists between the
proportion of male students who live on campus and the proportion of female students
who live on campus?
13. In comparing the two standard deviations below, what is the test value and what are the
degrees of freedom that should be used?
Standard Deviation Number of values
Sample 1
6
18
Sample 2
3
23
14. One poll found that 46% of male voters will support a candidate while another found
that 49% of female voters will be in support. To test whether this candidate has equal
levels of support between male and female voters, what should the alternative
hypothesis be?
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Chapter 9 Test B
15. A study of cats and dogs found that 22 of 40 cats and 37 of 55 dogs slept more than 10
hours per day. At the .05 level of significance, is there sufficient evidence to conclude
that a difference exists between the proportion of cats and the proportion of dogs that
sleep more than 10 hours per day?
16. For the samples summarized below, test the hypothesis at α =.05 that the two variances
are equal.
Variance
Number of data values
Sample 1
25
10
Sample 2
10
20
17. A researcher hypothesizes that the variation in the car rental rates at a major cities'
airport is less than the car rental rates in that city. The variance of 9 airport car rental
rates was $30 and the variance of 5 city car rental rates was $60. What is the test value?
18. A reporter bought a hamburger at each of a set of random stores of two different
restaurant chains. She then had the number of calories in each hamburger measured.
Can the reporter conclude, at α = .05, that the two sets of hamburgers have a different
number of categories? (Use the equal variances formula)
Women
Men
Sample size
6
9
Mean spending amount
80
135
Sample variance
600
900
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Chapter 9 Test B
19. A medical researcher is interested in whether patients' left arms or right arms are longer.
If 8 patients participate in this study (so that n left arms and n left arms are measured),
how many degrees of freedom should the researcher use in her t-test critical value?
20. A marketing firm asked a random set of married women and married men as to how
much they were willing to spend for jewelry as a present to their spouse. Can the firm
conclude, at α = .05, that the two groups have different willingness to spend? (Use the
unequal variances formula)
Women
Men
Sample size
8
14
Mean spending amount
80
55
Sample variance
45
600
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Chapter 9 Test B
Answer Key
1. p  52 and q  43
95
95
2. F-test: H0: 12   22 ; C.V. = 2.62; Fail to reject H , therefore it can be assumed that the
0
variances are equal. t-test H 0 : 1  2 H1 : 1  2 , t = -1.84, C.V. = 2.110 , fail to reject
reject H0. There is not enough evidence to support the claim that the two agencies are
not the same.
3. H0 : 1   2 H1: 1   2
. . Reject H0 . It appears that the
Critical Value = 2.33, z  599
average water level in Horseshoe Lake is more than the average water level in Swan
Lake.
4. H0 : 1   2 H1: 1   2 . Critical Value = ±1.96; z  379
. . Reject H0 . There is a
difference in price between the two stores.
5. F -test: H 0 :  12   22 ; C.V. = 3.02; Fail to reject H 0 , therefore it can be assumed that the
variances are equal. t-test: H0 : 1  2 H1 : 1  2 , t = 5.20, C.V.= 2.500 , reject H0.
There is enough evidence to support the claim that River Heights donates more money.
6. Accept the hypothesis because the test value 2.67 is less than the critical value 2.88.
7. p = 0.32 and q = 0.68
8. test value = 1.43, degrees of freedom = 11 and 25
9. –1.79
10. H0 : psycholog y  biolog y
11. Yes, because the test value –3.62 is outside the range (-3.25, 3.25).
12. Yes, there is sufficient information to reject the hypothesis that the proportion of male
students who live on campus and the proportion of female students who live on campus
are the same because the test value –2.33 is outside the acceptance region (-1.96,1.96).
13. test value = 4.00, degrees of freedom = 18 and 23
14. H0 : pmale  pfemale
15. No, there is not sufficient information to reject the hypothesis that the proportion of cats
and the proportion of dogs that sleep more than 10 hours per day are the same because
the test value –1.22 is inside the acceptance region (-1.96,1.96).
16. Accept the hypothesis because the test value 2.50 is less than the critical value 2.88.
17. 2.00
18. Yes, because the test value –3.73 is outside the interval (-2.16, 2.16)
19. 7
20. Yes, because the test value 3.59 is outside the interval (-2.36, 2.36)
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