# Chapter 9 - Waterford High School

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```					     Chapter 9 - Testing the Difference Between Two Means, Two
Variances, and Two Proportions
1. If the test value in the figure below, for a test of the difference between two large
sample means, is 2.57 when the critical value is 1.96, what decision about the

A) reject the null hypothesis       C) reject the alternative hypothesis
B) accept the null hypothesis       D) not enough information
Ans: A Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-3

2.                                                                    1       2

n2 n1
The standard error of difference of two large sample means is    .
Ans: False Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-2

3. In the figure below, if the z -test value is 1.43 for a test of the difference between two
large sample means, then the null hypothesis should not be rejected.

Ans: True   Difficulty: Easy     Objective: 1     Section: 2    Similar Exercise: 9-2-3

4. When hypothesizing a difference of 0, if the confidence interval does not contain 0, the
null hypothesis is rejected.
Ans: True Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-4

5. For normally distributed populations, if two samples are independent and the variances
are known, the z -test is used.
Ans: True Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-3

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6. A pharmaceutical company is testing the effectiveness of a new drug for lowering
cholesterol. As part of this trial, they wish to determine whether there is a difference
between the effectivess for women and for men. At α = .05, what is the test value?
Women                Men
Sample size                           70                  70
Mean effect                           8.5                8.65
Sample variance                       2.5                 4.5
A) –1.50 B) 0.32 C) –2.11 D) –0.47
Ans: D Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6

7. The campus bookstore asked a random set of freshmen and seniors as to how much they
spent on textbooks in that term. The bookstore believes that the two groups spend the
same amount. What is the test value?
Freshmen                Seniors
Sample size                        70                    60
Mean spending                      40                    25
Sample variance                   400                   800
A) 0.79 B) 4.36 C) 3.44 D) 2.00
Ans: C Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6

Use the following to answer questions 8-10:

A sociologist wants to determine if the life expectancy of people in Africa is less than
the life expectancy of people in Asia. The data obtained is shown in the table below.

Africa       Asia
X        55.3         65.2
        8.1          9.3
n        53           42

8. What is the null hypothesis? Use   0.05 .
A) H0 :  1   2 B) H0 : 1   2 C) H0 :  1   2 D) H0 :  1   2
Ans: B Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6

9. Calculate the critical value. Use   0.05 .
A) –1.65 B) –2.33 C) –2.58 D) –1.96
Ans: A Difficulty: Easy Objective: 1 Section: 2                    Similar Exercise: 9-2-6

10. What is the test value? Use   0.05 .
A) –6.86 B) –3.70 C) –4.13 D) –5.45
Ans: D Difficulty: Moderate Objective: 1                 Section: 2     Similar Exercise: 9-2-
6

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11. Determine the 95% confidence interval of the true difference in the means. A sociologist
wants to determine if the life expectancy of people in Africa is less than the life
expectancy of people in Asia. The data obtained is shown in the table below. Use
  0.05 .
Africa       Asia
X         55.3         65.2
          8.1          9.3
n          53           42
A)     1216  1   2  6.86
.                                  C)     1135  1   2  7.58
.
B)     13.46  1   2  6.34              D) 16.33  1   2  5.98
Ans: B Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-
19

12. The formula for the z -test for comparing two means from independent populations is
__________.
Ans:     X 1  X 2    1  2 
t
 12       2
2

n1         n2
Difficulty: Moderate             Objective: 1   Section: 2   Similar Exercise: 9-2-2

13. 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
x      \$650               \$730
      \$61                \$78
n      24                 21
Ans: H0: 1   2 H1: 1   2 . Critical Value = ±1.96; z  3.79 . Reject H0 . There is a
difference in price between the two stores.
Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-6

14. 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
x     43                              38
      3.2                             2.4
n     23                              23
Ans:   H0 : 1   2 H1: 1   2 Critical Value = 2.33, z  5.99 . Reject H0 . It appears
that the average water level in Horseshoe Lake is more than the average water
level in Swan Lake.
Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-6

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15. A marketing firm asked a random set of married and single men as to how much they
were willing to spend for a vacation. At α = .05, is a difference in the two amounts?
Married men            Single men
Sample size                          60                     40
Mean spending                       420                    405
Sample variance                    5500                   8000
A) No, because the test value 0.05 is inside the interval (-1.96, 1.96)
B) No, because the test value 0.88 is inside the interval (-1.96, 1.96)
C) No, because the test value 1.45 is inside the interval (-1.96, 1.96)
D) No, because the test value 1.45 is outside the interval (-1.96, 1.96)
Ans: B Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-
6

16. A bond analyst is analyzing the interests rates for equivalent municipal bonds issued by
two different states. At α = .05, is there a difference in the interest rates paid by the two
states?
State A                State B
Sample size                          40                    50
Mean interest rate (%)               3.9                  4.35
Sample variance                     0.03                  0.04
A) Yes, because the test value –11.43 is outside the interval (-1.96, 1.96)
B) Yes, because the test value –2.90 is outside the interval (-1.96, 1.96)
C) Yes, because the test value 130.65 is outside the interval (-1.96, 1.96)
D) No, because the test value –0.01 is inside the interval (-1.96, 1.96)
Ans: A Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-
6

17. An educational researcher is analyzing the test scores for statistics students taught using
two different methods - a traditional method and a web-based self-paced method. Can
he conclude, at α = .05, that the test scores in the web-based self-paced method are
lower?
Sample size                            40                       80
Mean test score                        80                       77
Sample variance                        28                       32
A) The data does not support the claim because the test value 1.36 is less than than
1.64.
B) The data does not support the claim because the test value 1.36 is less than than
1.96.
C) The data supports the claim because the test value 2.86 is greater than than 1.96.
D) The data supports the claim because the test value 2.86 is greater than than 1.64.
Ans: D Difficulty: Hard Objective: 1 Section: 2 Similar Exercise: 9-2-6

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18. An field researcher is gathering data on the trunk diameters of mature pine and spruce
trees in a certain area. The following are the results of his random sampling. Can he
conclude, at α = .10, that the average trunk diameter of a pine tree is greater than the
average diameter of a spruce tree?
Pine trees            Spruce trees
Sample size                            80                     60
Mean trunk diameter (cm)               45                     42
Sample variance                       140                    180
A) The data does not support the claim because the test value 0.63 is less than than
1.28.
B) The data does not support the claim because the test value 1.38 is greater than
than 1.28.
C) The data does not support the claim because the test value 1.38 is less than than
1.64.
D) The data does not support the claim because the test value 0.63 is less than than
1.64.
Ans: B Difficulty: Hard Objective: 1 Section: 2 Similar Exercise: 9-2-6

19. The value of F cannot be negative, because variances are always positive or zero.
Ans: True Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4

20. When finding the F -test value, the smaller of the variances is placed in the numerator.
Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-1

21. When comparing two variances or standard deviations, a t -test is used.
Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-1

22. The critical value for a one-tailed right F -test is 2.57, when   0025 , the degrees of
.
freedom for the numerator = 15, and the degrees of freedom for the denominator = 20.
Ans: True Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-5

23. The critical value for a two-tailed F -test is 2.65, when   0.05 , the sample size from
which the variance for the numerator was obtained = 10, and the sample size from
which the variance for the denominator was obtained = 15.
Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-5

24. The mean value of F is approximately equal to __________.
Ans: one
Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4

25. To determine whether two sample variances are equal, a researcher can use a(n)
__________.
Ans: F-test
Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4

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26. 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                     17
Sample 2                       9                     28
A) test value = 0.78, degrees of freedom = 17 and 28
B) test value = 0.78, degrees of freedom = 16 and 27
C) test value = 1.29, degrees of freedom = 16 and 27
D) test value = 1.29, degrees of freedom = 17 and 28
Ans: C Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-7

27. For the samples summarized below, test the hypothesis at α =.05 that the two variances
are equal.
Variance         Number of data values
Sample 1                   19                      8
Sample 2                   7                      18
A) Accept the hypothesis because the test value 2.71 is less than the critical value
3.16.
B) Reject the hypothesis because the test value 2.71 is less than the critical value
3.16.
C) Reject the hypothesis because the test value 7.37 is greater than the critical value
3.01.
D) Reject the hypothesis because the test value 7.37 is greater than the critical value
3.01.
Ans: A Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-7

28. What is the critical value for a two-tailed F -test with   010 , when the sample size
.
from which the variance for the numerator was obtained was 10, and the sample size
from which the denominator was obtained was 24?
A) 2.27 B) 2.25 C) 2.32 D) 2.30
Ans: C Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-
5

29. Compute the critical value for a right-tailed F -test with   0.05 , d.f.N. = 21, and
d.f.D. = 20.
A) 2.12 B) 2.23 C) 2.20 D) 2.16
Ans: A Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-
5

30. A car salesman claims that the variance of prices on convertibles is higher than the
variance on station wagons. The standard deviation of 16 convertibles is \$6800 and the
standard deviation of 24 station wagons is \$3900. For   0.05 , what is the test value?
A) 3.00 B) 3.04 C) 2.78 D) 2.33
Ans: B Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-
8

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31. A researcher hypothesizes that the variation in the amount of money spent on business
dinners is greater than the amount of money spent on lunches. The variance of nine
business dinners was \$6.12 and the variance of 12 business lunches was \$0.87. What is
the test value?
A) 3.1 B) 9.61 C) 49.5 D) 7.03
Ans: D Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-
8

32. 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 10 airport car rental
rates was \$25 and the variance of 4 city car rental rates was \$60. What is the test value?
A) 6.00 B) 1.55 C) 2.40 D) 5.76
Ans: C Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-
8

33. Determine the value of  as shown in the figure below, if the degrees of freedom were
seven and nine.

A) 0.01 B) 0.025 C) 0.05              D) 0.1
Ans: B Difficulty: Moderate           Objective: 2      Section: 3      Similar Exercise: 9-3-
5

34. If the variances are not known and one or both sample sizes are less than 30, the F -test
must be used.
Ans: False Difficulty: Moderate Objective: 2 Section: 3
Similar Exercise: 9-3-4

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35. If s1  12.31 and F  2.13 , what is the value of s2 as shown in the figure below?

A) 5.78 B) 8.43 C) 71.14              D) 17.97
Ans: B Difficulty: Moderate           Objective: 2      Section: 3      Similar Exercise: 9-3-
5

36. For the samples summarized below, test the hypothesis at α =.05 that the two variances
are equal.
Variance         Number of data values
Sample 1                   26                      7
Sample 2                   11                     17
A) Accept the hypothesis because the test value 5.59 is greater than the critical value
3.34.
B) Reject the hypothesis because the test value 2.36 is less than the critical value
3.16.
C) Reject the hypothesis because the test value 5.59 is greater than the critical value
3.16.
D) Accept the hypothesis because the test value 2.36 is less than the critical value
3.34.
Ans: D Difficulty: Hard Objective: 2 Section: 3 Similar Exercise: 9-3-7

37. 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                        5                  20
Sample 2                        4                  28
A) test value = 1.25, degrees of freedom = 20 and 28
B) test value = 1.25, degrees of freedom = 19 and 27
C) test value = 1.56, degrees of freedom = 20 and 28
D) test value = 1.56, degrees of freedom = 19 and 27
Ans: C Difficulty: Hard Objective: 2 Section: 3 Similar Exercise: 9-3-7

38. A pooled estimate of the variance is a weighted average of the variance using the two
sample variances and the __________ of each variance as the weights.
Ans: degrees of freedom
Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 9-3-3

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39. 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 12 psychology students was 3.5 and the average grade
average of a sample of 11 biology students was 3.6. What is the null hypothesis for this
study?
A) H0 :   3.5 and 3.6
B)    H0 : psycho log y  3.5 and H0 : bio log y  3.6
C)    H0 : psycho log y  bio log y  7.1
D) H0 : psycho log y  bio log y
Ans: D Difficulty: Easy Objective: 3                           Section: 4   Similar Exercise: 9-4-1

Use the following to answer questions 40-42:

Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the
average price of imported wine is less than the average price of domestic wine. The
data obtained is shown in the table below.

Imported Wine                      Domestic Wine
X     7.03                                 9.78
s     2.31                                 3.62
n     15                                   16

40. What is the null hypothesis? Use   0.05 .
A) H0 :  1   2 B) H0 : 1   2 C) H0 :  1   2 D) H0 :  1   2
Ans: B Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 9-4-1

41. What is the critical value? Use   0.05 .
A) –1.761 B) –2.045 C) –1.697 D) –1.703
Ans: A Difficulty: Moderate Objective: 3 Section: 4                             Similar Exercise: 9-4-
1

42. What is the test value? Use   0.05 . (Use the variances unequal formula)
A) –6.97 B) –2.50 C) –4.53 D) –2.54
Ans: D Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-
Rev-10

43. The formula for the t - test for comparing two means (independent samples, variances

equal) is: t 
X   1        
 X 2   1  2 
.
2
s  s2
1
 2
n1 n2
Ans: False Difficulty: Moderate                       Objective: 3    Section: 4
Similar Exercise: 9-4-1

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44. In testing the equality of the two means below, what is the test statistic? (Use the
unequal variances formula)
Sample 1              Sample 2
Sample size                        10                    11
Sample mean                        80                    75
Sample variance                   600                   100
A) 2.26 B) 0.17 C) 0.07 D) 0.60
Ans: D Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-
Rev-10

45. In testing the equality of the two means below, what is the test statistic? (Use the equal
variances formula)
Sample 1              Sample 2
Sample size                        13                     9
Sample mean                        55                    80
Sample variance                   600                   400
A) –2.53 B) –1.50 C) –0.26 D) –2.31
Ans: A Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-4-
1

46. 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
x    \$35                             \$25
s    \$5                              \$8
n    24                              24
Ans: F -test: H 0 : 1   2 ; C.V. = 3.02; Fail to reject H 0 , therefore it can be assumed
2     2

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.
Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-1

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47. 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
x    \$6.25                     \$6.55
s    \$0.40                     \$0.58
n    18                        20
Ans: F-test: H0 : 1   2 ; C.V. = 2.62; Fail to reject H , therefore it can be assumed
2     2
0
that the variances are equal. t-test H0 : 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.
Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-1

48. 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                         10                    14
Mean spending amount                80                   115
Sample variance                     55                   600
A) No, because the test value –0.72 is inside the interval (-2.23, 2.23)
B) Yes, because the test value –5.03 is outside the interval (-2.26, 2.26)
C) Yes, because the test value –10.91 is inside the interval (-2.23, 2.23)
D) No, because the test value –10.91 is outside the interval (-2.26, 2.26)
Ans: B Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-Rev-10

49. 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                          7                    8
Mean spending amount                80                   95
Sample variance                    450                  900
A) No, because the test value –0.08 is inside the interval (-2.14, 2.14)
B) No, because the test value –0.08 is inside the interval (-2.16, 2.16)
C) No, because the test value –1.10 is inside the interval (-2.16, 2.16)
D) No, because the test value –2.00 is inside the interval (-2.16, 2.16)
Ans: C Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-2

50. When subjects are matched according to one variable, the matching process does not
eliminate the influence of other variables.
Ans: True Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-1

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51. Samples are independent when they are not related.
Ans: True Difficulty: Easy Objective: 4 Section: 5                    Similar Exercise: 9-5-1

52. A medical researcher is interested in whether patients' left arms or right arms are longer.
If 9 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?
A) 8 B) 9 C) 16 D) 17
Ans: A Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-2

53. When the subjects are paired or matched in some way, samples are considered to be
__________.
Ans: dependent
Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-1

Use the following to answer questions 54-57:

A researcher wanted to determine if using an octane booster would increase gasoline
mileage. A random sample of seven cars was selected; the cars were driven for two
weeks without the booster and two weeks with the booster.

Miles / Gal Without              Miles / Gal With
21.2                             23.8
25.4                             25.6
20.9                             22.4
27.6                             28.3
22.8                             24.5
27.3                             28.8
23.4                             25.2

54. State the alternative hypothesis?
A) H1:  D  0 B) H1:  D  0 C) H1:  D  0 D) H1:  D  0
Ans: C Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-2

55. Determine the mean of the difference.
A) –0.96 B) –6.3 C) 1.43 D) –1.43
Ans: D Difficulty: Moderate Objective: 4                 Section: 5     Similar Exercise: 9-5-
2

56. Compute the standard deviation of the difference.
A) 0.78 B) 0.69 C) 0.87 D) 0.48
Ans: A Difficulty: Moderate Objective: 4 Section: 5                     Similar Exercise: 9-5-
2

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57. What is the critical value using   0.05 ?
A) -1.782 B) -1.761 C) -1.943 D) -1.895
Ans: C Difficulty: Moderate Objective: 4 Section: 5                     Similar Exercise: 9-5-
2

58. If the samples are dependent, the t - test for dependent samples is used.
Ans: True Difficulty: Moderate Objective: 4 Section: 5
Similar Exercise: 9-5-1

59. The formula of the t -test for dependent samples is __________.
Ans:    D  D
t
sD
n
Difficulty: Moderate       Objective: 4     Section: 5      Similar Exercise: 9-5-1

60. The critical value for a left-tailed t-test for dependent samples is __________ when the
degrees of freedom = 7 and   0025 .
.
Ans: –2.365
Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5-2

61. A running coach wanted to see whether runners ran faster after eating spaghetti the night
before. 14 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                         940               930              –10
Sample variance                    3000              2000              450
A) –1.87 B) –0.47 C) –0.14 D) –1.76
Ans: D Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5-
2

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62. A dietician investigated whether apples washed in hot water or in cold water turned
brown at different rates when exposed to air. She took 11 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                         5.00              4.35             –0.65
Sample variance                     1.60              2.00              0.55
A) No, because the test value –0.83 is inside the range (-3.11, 3.11).
B) No, because the test value –2.91 is inside the range (-3.17, 3.17).
C) No, because the test value –2.91 is inside the range (-3.11, 3.11).
D) No, because the test value –0.83 is inside the range (-3.17, 3.17).
Ans: B Difficulty: Hard Objective: 4 Section: 5 Similar Exercise: 9-5-2

63. One of the requirements for the z - test for comparing two proportions is that the
samples must be dependent on each other.
Ans: False Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3

64. One poll found that 43% 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, the null hypothesis should be
A) H0 : pmale  pfemale                       C)    H0 : pmale  43%, H0 : pfemale  49%
B)     H0 : pmale  50%, H0 : pfemale  50% D) H0 : pmale  pfemale
Ans: A Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3

65. One poll found that 38% of male voters will support a candidate while another found
that 44% of female voters will be in support. To test whether this candidate has equal
levels of support between male and female voters, the alternative hypothesis should be
A) H0 : pmale  pfemale
B)     H0 : pmale  50%, H0 : pfemale  50%
C)     H0 : pmale  38%, H0 : pfemale  44%
D) H0 : pmale  pfemale
Ans: D Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3

66. Find p and q , if x1  23, n1  43, x2  29, and n2  52 .
Ans: p  52 and q  43
95         95
Difficulty: Easy     Objective: 5      Section: 6      Similar Exercise: 9-6-2

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67. Find   p and q when X 1 =12, n1 =40, X 2 =20, and n2 =60
A)      p = 0.32 and q = 0.68                C)    p = 1.47 and q = 3.12
B)      p = 3.12 and q = 1.47                D)    p = 0.68 and q = 0.32
Ans:   A Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-1

68. A recent survey reported that in a sample of 300 students who attend two-year colleges,
105 work at least 20 hours a week. In a sample of 225 students attending private
universities, only 20 students work at least 20 hours per week. What is the test value?
A) 6.95 B) 7.61 C) 2.38 D) 4.18
Ans: A Difficulty: Moderate Objective: 5 Section: 6 Similar Exercise: 9-6-
3

69. The standard error of difference in terms of the weighted estimate is __________ when
testing the difference between two population proportions.
Ans:                1 1
 ( p  p )  pq            
 n1       n2 
1   2

Difficulty: Moderate              Objective: 5   Section: 6   Similar Exercise: 9-6-3

70. When testing the difference between two proportions, one sample had 30 out of 100
who were for capital punishment and the other sample had 60 out of 80 who were for
capital punishment. Calculate the standard error.
A) 0.075 B) 0.060 C) 0.042 D) 0.098
Ans: A Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5

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71. 70% of students at a university live on campus. A random sample found that 31 of 50
male students and 41 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?
A) No, there is not 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 –0.20 is inside the acceptance
region (-1.96,1.96).
B) No, there is not 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 –1.21 is inside the acceptance
region (-1.96,1.96).
C) 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).
D) 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 –2.23 is outside the acceptance
region (-1.96,1.96).
Ans: D Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5

72. Many elementary school students in a school district currently have ear infections. A
random sample of children in two different schools found that 16 of 40 at one school
and 13 of 30 at the other had this infection. At the .05 level of significance, is there
sufficient evidence to conclude that a difference exists between the proportion of
students who have ear infections at one school and the other?
A) Yes, there is sufficient information to reject the hypothesis that the proportions of
students at the two schools who have ear infections are the same because the test
value –2.35 is outside the acceptance region (-1.96,1.96).
B) No, there is not sufficient information to reject the hypothesis that the proportions
of students at the two schools who have ear infections are the same because the
test value –0.28 is inside the acceptance region (-1.96,1.96).
C) No, there is not sufficient information to reject the hypothesis that the proportions
of students at the two schools who have ear infections are the same because the
test value –0.37 is inside the acceptance region (-1.96,1.96).
D) No, there is not sufficient information to reject the hypothesis that the proportions
of students at the two schools who have ear infections are the same because the
test value –1.32 is inside the acceptance region (-1.96,1.96).
Ans: B Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5

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73. A study of cats and dogs found that 16 of 50 cats and 32 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?
A) Yes, there is 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 –2.69 is outside the acceptance region (-1.96,1.96).
B) 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 –1.76 is inside the acceptance region (-1.96,1.96).
C) Yes, there is 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 –3.11 is outside the acceptance region (-1.96,1.96).
D) 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 –0.84 is inside the acceptance region (-1.96,1.96).
Ans: A Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5

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