Chapter 9 - Waterford High School

					     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
   hypothesis should be made?




     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?
                                             Traditional       Web-based Self-paced
           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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     Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions


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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     Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions


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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