CHAPTER 10 by QdIe2NaD

VIEWS: 8 PAGES: 10

									                                                                                         CHAPTER 9
                                                 TESTS OF HYPOTHESIS: SMALL SAMPLES

1.   a.      Reject Ho where t > 1.833
                 12  10
     b.      t             2.108
                (3 / 10 )
     c.      Reject Ho, the mean is greater than 10.

2.   a.      Reject Ho if t < 3.106 or t > 3.106
                407  400
     b.      t               4.042
                 (6 / 12 )
     c.      Reject Ho, the mean does not equal 400.

3.   Ho:   40       H1:  > 40     Reject Ho if t > 1.703
           42  40
     t               5.040
         (2.1 / 28 )
     Reject Ho and conclude that the mean number of calls is greater than 40 per week.

4.   Ho:   42.3 H1:  < 42.3 Reject Ho if t < 1.319
         40.6  42.3
     t               3.084
         (2.7 / 24 )
     Reject Ho. The mean assembly time is less than 42.3 minutes.

5.   Ho:   22,100          H1:  > 22,100            Reject Ho if t > 1.740
         23,400  22,100
     t                   3.680
          (1500 / 18 )
     Reject Ho and conclude that the mean life of the spark plugs is greater than 22,100 miles.

6.   Ho:   15      H1:  > 15      Reject Ho if t > 1.725
          18  15
     t            13.75
         (1 / 21)
     Reject Ho and conclude that the mean service time is greater than 15 minutes.

7.   a.      Reject Ho if t < 3.747
                                     (85) 2
                               1495 
                                       5  3536                  17  20
     b.      X  17 and s                    .             t              190
                                                                               .
                                  51                            .
                                                                3536 / 5
     c.      Do not reject Ho. We cannot conclude the population mean is less than 20.
     d.      Between 0.05 and 0.10, about 0.065




                                                 85                                    Chapter 9
8.      a.      Reject Ho if t < 2.571 or t > 2.571
                    111667  100
                        .
        b.       t                 4.72
                      6.055 / 6
        c.      Reject Ho. The population mean is not equal to 100
        d.      less than 0.01 (between 0.001 and 0.01)

9.      Ho:   4.35            H1:  > 4.35             Reject Ho if t > 2.821
             4.368  4.35
        t                  168
                              .
            (0.0339 / 10 )
        Do not reject Ho. The additive did not increase the mean weight of the chickens. The p-value is
        between 0.10 and 0.05.

10.     Ho:   2160            H1:  > 2160             Reject Ho if t > 2.306
            2172.44  2160
        t                  3.98
             (9.3823 / 9 )
        Reject Ho. The mean chlorine shelf life has increased. The p-value is less than 0.005.

11.     Ho:   4.0              H1:  > 4.0           Reject Ho if t > 1.796
             4.50  4.0
        t                 0.65
            (2.68 / 12 )
        Do not reject Ho. Mean number of fish caught has not been shown to be greater than 4.0. The p-
        value is greater than 0.10.

12.     Ho:   53              H1:  > 53           Reject Ho if t > 1.761
              56.4  53.0
        t                  352
                              .
            (3.7378 / 15 )
        Reject Ho. The mean number of surveys conducted is greater than 53. The p-value is less than
        0.005.

13.     a.      Reject Ho if t > 2.120 or t < 2.120      df = 10 + 8 – 2 = 16
                     (10  1)(4)  (8  1)(5)
                                 2            2
        b.      s2                              19.9375
                             10  8  2
                 p

                          23  26
        c.      t                       1416
                                             .
                             F I
                             G J 1 1
                                   
                     19.9375
                             H K10 8
        d.      Do not reject Ho.
        e.      p-value is greater than 0.10 and less than 0.20




Chapter 9                                           86
14.   a.      Reject Ho if t > 1.697 or t < 1.697      df = 17 + 15 – 2 = 30
                   (15  1)(12)  (17  1)(15)
                                2              2
      b.      s2                                 187.20
                             15  17  2
               p

                      350  342
      c.      t                       1651
                                         .
                          F
                          G 1
                              
                                  1I
                                   J
                   187.2
                          H15 17   K
      d.      Do not reject Ho.
      e.      p-value is greater than 0.10 and less than 0.20

15.   Ho: f  m              H1: f > m       df = 9 + 7 – 2 = 14       Reject Ho if t > 2.624
           (7  1)(6.88)  (9  1)(9.49)
                        2                2
                                                                            79  78
      s2                                   71749
                                               .                  t                      0.234
       p
                      972                                                    F I
                                                                               G J
                                                                         71.749 
                                                                                 1 1
                                                                               H K
                                                                                 7 9
      Do not reject Ho. There is no difference in the mean grades.

16.   Ho: s  d               H1: s > d      df = 15 + 12 – 2 = 25 Reject Ho if t > 2.485
           (15  1)(155) 2  (12  1)(181) 2
                      .                 .                               61  48.4
      s2                                     278.69             t                     1.949
       p
                     15  12  2                                              1F
                                                                               G
                                                                                  1     I
                                                                                        J
                                                                    278.69
                                                                               H
                                                                             15 12      K
      Do not reject Ho. There is no difference in the mean amount of time spent watching television.

17.   Ho: s  a              H1: s> a       df = 6 + 7 – 2 = 11     Reject Ho if t > 1.363
           (6  1)(12.2)  (7  1)(158)
                        2
                                     .  2
                                                                     142.5  130.3
      s2                                  20382
                                               .                 t                    1536
                                                                                         .
       p
                      672
                                                                     20382 
                                                                               F I
                                                                               G J
                                                                             1 1
                                                                         .
                                                                               H K
                                                                             6 7
      Reject Ho. The mean daily expenses are greater for the sales staff. The p-value is between 0.05
      and 0.10.

18.   Ho: n  t                H1: n > t      df = 12 + 8 – 2 = 18  Reject Ho if t > 2.552
           (12  1)(22.8) 2  (8  1)(34.4) 2                         5358  526.8
                                                                          .
      s2                                      777.88             t                   0.707
       p
                      12  8  2
                                                                     777.88 
                                                                               F I
                                                                               G J
                                                                             1 1
                                                                               H K
                                                                             8 12
      Do not reject Ho. There is no difference in the mean salary of nurses and elementary school
      teachers. The p-value is greater than 0.10.

19.   a.      Reject Ho if t > 2.353
                                                      (12) 2
                                               38 
                   12                                   4  0.816
      b.       d       3.00           sd 
                    4                                 3
                      3.00
      c.      t               7.35
                  0.816 / 4
      d.      Reject the Ho. There are more defective parts produced on the day shift.
      e.      p-value is less than 0.005, but greater than 0.0005



                                                    87                                     Chapter 9
20.     a.       Reject Ho if t < 2.776 or t > 2.776
                                                         (23) 2
                                                 115 
                      23                                   5  152
        b.       d        4.6            sd                  .
                       5                                4
                         4.6
        c.       t              6.767
                      .
                     152 / 5
        d.       Reject the Ho. There is a difference in the mean number of citations given by the two
                 officers.
        e.       p-value is less than 0.01, but greater than 0.001

21.     Ho: d  0             H1: d > 0      Reject Ho if t > 2.764
        d = 7.3636             sd = 8.3699
               7.3636
        t               2.92         Reject Ho. The weights have increased
            8.3699 / 11

22.     Ho: d  0             H1: d > 0        Reject Ho if t > 1.796
        d = 25.917              sd = 40.791
               25.917
        t               2.20
            40.791 / 12
        Reject Ho. The incentive plan resulted in an increase in daily income. The p-value is about
        0.025.

23.     Ho: d  0                H1: d > 0      Reject Ho if t > 2.821
        d = 0.10                  sd = 4.28
                .
               010
        t             0.07              Fail to reject Ho. There has been no reduction.
            4.28 / 10

24.     Ho: d  0     H1: d < 0         Reject Ho if t < 2.998
        d = 3.625     sd = 4.8385
               3.625
        t              2.12            Do not reject Ho. The p-value is about 0.035
            4.8385 / 8

25.     Ho:   87       H1:  < 87       Reject Ho if t < 1.895
            664                                 55,244  (664) 2 / 8
            X    83.0                   s                          4.3425
              8                                        81
             83  87
        t               2.61           Reject Ho. The mileage is less than advertised.
           4.3425 / 8

26.     Ho:   42       H1:  > 42    Reject Ho if t > 1.796
            51  42
        t           3.90
           8 / 12
        Reject Ho. The mean time for delivery is more than 42 days. The p-value is less than 0.005




Chapter 9                                               88
27.   Ho:   9        H1:  > 9     Reject Ho if t > 2.998
       X = 9.488       s = 0.467
          9.488  9.00
      t                2.95
           0.467 / 8
      Do not reject Ho. The mean prime rate for small banks is 9.0 percent. The p-value is less than
      0.025.

28.   Ho:  =2.25     H1:   2.25 Reject Ho if t < 2.201 or t > 2.201
      X = 2.087       sd = 0.4048
          2.087  2.25
      t                1395
                            .
          0.4048 / 12
      Do not reject Ho. There is not a difference in the mean amount of coffee consumed at
      Northwestern State.

29.   Ho:   25      H1:  > 25    Reject Ho if t > 2.624
      X = 26.07       s = 1.5337
          26.07  25.00
      t                 2.702
           .
          15337 / 15
      Reject Ho. The mean number of patients per day is more than 25. The p-value is less than 0.01.

30.   Ho:   6.5     H1:  < 6.5     Reject Ho if t < 2.718
      X = 5.1667      s = 3.1575
          51667  6.5
            .
      t                 1463
                            .
           .
          31575 / 12
      Do not reject Ho.

31.   Ho:   3.5     H1:  < 3.5   Reject Ho if t < 1.746
                                        2.9553  35 .
      X  2.9553     s= 0.5596       t                4.013
                                        0.5596 / 17
      Reject Ho. The mean time to complete a game is less than 3.5 hours.

32.   Ho:  =0        H1:   0      Reject Ho if t < 2.110 or t > 2.110
       X = 0.2322 s = 0.3120
          0.2322  0
      t                3158
                           .
          0.3120 / 18
      Reject Ho. The mean gain or loss does not equal 0. The p-value is less than 0.01, but greater than
      0.001.

33.   Ho:   4.5%            H1:  > 4.5%           Reject Ho if t > 1.796
      X = 4.5717      s = 0.2405
          4.5717  4.50
      t                 1033
                           .
          0.2405 / 12
      Do not reject Ho. The mean number rate of return is not more than 4.5%.




                                                 89                                    Chapter 9
34.     Ho: 1 = 2               H1: 1  2            Reject Ho if t < 2.060 or t > 2.060
             (15  1)(2.6)  (12  1)(3.3) 2
                          2
                                                                                   17.6  16.2
        s2                                   8.5772                      t                     123
                                                                                                    .
         p
                       15  12  2                                                        F
                                                                                          G
                                                                                          1
                                                                                            
                                                                                               1      I
                                                                                                      J
                                                                                8.5772
                                                                                          H
                                                                                         15 12        K
        Do not reject Ho. There is no difference in the mean percent of salaries spent by employees on
        the two health packages.

35.     Ho: e  b               H1: e > b           Reject Ho if t > 1.701
             (20  1)(584)  (10  1)(5.67)
                       .    2               2
                                                                                      24.80  20.25
        s2                                    33.4767                   t                               2.031
         p
                         20  10  2                                                       F 1I
                                                                                    33.4767G  J
                                                                                            1
                                                                                           H 20K
                                                                                           10
        Ho is rejected. The mean weight of the packages at the end of the month is larger.

36.     Ho: n = s               H1: n  s              Reject Ho if t < 2.086 or t > 2.086
              (10  1)(10.5)  (12  1)(14.25)
                            2                  2
                                                                             8355  78.8
                                                                               .
         s2                                      1612969
                                                      .            t                          0.874
          p
                         10  12  2                                                1F
                                                                                     G  
                                                                                          1   I
                                                                                              J
                                                                             .
                                                                          1612969
                                                                                     H
                                                                                   10 12      K
        Do not reject Ho. There is no difference in the mean number of hamburgers sold at the two
        locations.

37.     Ho: 1  2               H1: 1 > 2              Reject Ho if t > 2.567
              (8  1)(2.2638)  (11  1)(2.4606)
                             2                   2
                                                                         10.375  5.636
        s2                                         5.672         t                    4.28
          p
                           8  11  2                                           F I
                                                                                G J
                                                                                1 1
                                                                          5.672 
                                                                                H K
                                                                                8 11
        Reject Ho. The mean number of transaction by the young adults is more than for the senior
        citizens.

38.     Ho: 1 = 2               H1: 1  2                Reject Ho if t > 2.086 or t < 2.086
        X 1 =12.17        s1 = 1.0563     X 2 = 14.875       s2 = 2.2079
               (10  1)(10563) 2  (12  1)(2.2079) 2
                         .                                                           12.17  14.875
        s2                                            31832
                                                         .                    t                       3541
                                                                                                          .
         p
                           10  12  2                                                   F 1I
                                                                                    31832G  J
                                                                                          1
                                                                                     .
                                                                                         H 12 K
                                                                                         10
        Reject Ho. There is a difference in the mean race times.

39.     Ho: 1  2               H1: 1 > 2           Reject Ho if t > 2.650
        X 1 =125.125      s1 = 15.094     X 2 = 117.714         s2 = 19.914
               (8  1)(15.094) 2  (7  1)(19.914) 2                               125125  117.714
                                                                                      .
        s2                                           305.708                t                       0.819
         p
                            872                                                          F 1I
                                                                                    305.708G J
                                                                                           1
                                                                                           H 7K
                                                                                           8
        Ho is not rejected. There is no difference in the mean number sold at the regular price and the
        mean number sold at reduced price.




Chapter 9                                               90
40.   Ho: 1 = 2              H1: 1  2             Reject Ho if t > 1.717 or t < 1.717
           (10  1)(13.68)  (14  1)(6.71) 2
                          2
                                                                        838  79.29
                                                                          .
      s2                                      10316
                                                   .           t                        1.07
       p
                      10  14  2                                           F
                                                                            G 1
                                                                                 
                                                                                    1 I
                                                                                      J
                                                                         .
                                                                      10316
                                                                            H10 14    K
      Do not reject Ho. There is no difference in the mean number of hours for the two treatments.

41.   Ho: 1 = 2              H1: 1  2             Reject Ho if t > 2.819 or t < 2.819
           (10  1)(2.33)  (14  1)(2.55) 2
                         2
                                                                      1587  18.29
                                                                        .
      s2                                     6.06            t                      2.374
       p
                      10  14  2                                        F
                                                                         G  1
                                                                              
                                                                                 1    I
                                                                                      J
                                                                         H
                                                                      6.06
                                                                           10 14      K
      Do not reject Ho. There is no difference in the mean amount purchased.

42.   Ho: d  0              H1: d < 0    Reject Ho if t < 2.998
      d = 2.5        sd = 2.928
             2.5
      t              2.415
          2.928 / 8
      Do not reject Ho. There mean number of accidents has not been reduced.

43.   Ho: d  0              H1: d > 0       Reject Ho if t > 1.895
       d = 1.75       sd = 2.9155
               .
              175
       t              1698
                         .
          2.9155 / 8
      Do not reject Ho. There is no difference in the mean number of absences. The p-value is greater
      than 0.05.

44.   Ho: d  0              H1: d > 0     Reject Ho if t > 1.796
      d = 0.1908      sd = 0.3260
              .
             01908
      t                2.027
          0.3260 / 12
      Reject Ho. The chip reduced the mean processing time. The p-value is greater than 0.025.

45.   Ho: d  0               H1: d > 0   Reject Ho if t > 1.833
      d = 0.027       sd = 0.2661
             0.027
      t                0.321
          0.2661 / 10
      Do not reject Ho. We have not shown a decline in grades.

46.   Ho: d = 0              H1: d  0       Reject Ho if t < 1.761 or t > 1.761
      d = 247.67             sd = 548.04
            247.67
      t                175
                           .
          548.04 / 15
      Do not reject Ho. There is no difference in the mean insurance price.




                                                      91                                  Chapter 9
47.     Ho: d  0              H1: d > 0       Reject Ho if t > 2.764
        d = 4.02        sd = 6.41
               4.02
        t             2.080
            6.41 / 11
        Do not reject Ho. Stock prices have not significantly increased.

48.     Answers will vary. Answer developed February 10, 1998
        Ho: d  0             H1: d > 0       Reject Ho if t > 1.860
        d = 2.99               sd = 3.38
               2.99
        t            2.654
            3.38 / 9
        Reject Ho. The mean price of the stock increased.

49.     a.      1 = without pool        2 = with pool
                Ho: 1 = 2              H1: 1  2             Reject Ho if t > 2.000 or t < 2.000
                X 1 = 202.79    s1 = 33.71       n = 38
                X 2 = 231.48    s2 = 50.48       n = 67
                      (38  1)(33.71)  (67  1)(50.48) 2
                                    2
                s2                                        204105
                                                                .
                                  38  67  2
                 p

                       202.79  231.48
                t                          312
                                               .
                               F
                               G1
                                    
                                       1I
                                        J
                      2041.05
                               H38 67   K
                Reject Ho. There is a difference in mean selling price for homes with and without a pool.
        b.      1 = without garage       2 = with garage
                Ho: 1 = 2               H1: 1  2             Reject Ho if t > 2.000 or t < 2.000
                 = 0.05                  df = 34 + 71 – 2 = 103
                X 1 = 185.44      s1 = 28.01       X 2 = 238.18 s2 = 44.88
                     (34  1)(28.01) 2  (71  1)(44.88) 2
                s2 
                 p                                          1620.25
                                     103
                      185.44  238.18
                t                         6.28
                               F
                               G1
                                  
                                      1 I
                                        J
                     1620.25
                               H
                               34 71    K
                Reject Ho. There is a difference in mean selling price for homes with and without a
                garage.




Chapter 9                                           92
      c.   Ho: 1 = 2                H1: 1  2            Reject Ho if t > 2.036 or t < 2.036
           X 1 = 196.92       s1 = 35.79      n = 15
           X 2 = 227.45       s2 = 44.2      n = 20
                (15  1)(35.79)  (20  1)(44.2) 2
                                 2
           s2                                      1668.24
                            15  20  2
            p

                          196.92  227.45
                   t                        2.188
                                    1F
                                     G
                                        1    I
                                             J
                         1668.24
                                     H
                                   15 20     K
           Reject Ho. There is a difference in mean selling price for homes in Township 1 and
           Township 2.

50.   a.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
                 (16  1)(34.3) 2  (14  1)(40.7) 2
            s2                                          1399.3471
                            16  14  2
             p

                     160.3  178.5             18.2
            t                                        1329
                                                           .
                           F
                           G    1
                                     
                                        1I
                                         J     13.69
                 1399.3471
                           H   16 14     K
           Do not reject Ho. There is no difference in mean number of home runs hit per team in the
           American League and the National League.
      b.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
                 (16  1)(0.0125)  (14  1)(0.0095)
                                      2                    2
            s2                                               0.0001256
                                16  14  2
             p

                     0.262  0.271             0.090
            t                                         2.194
                           F
                           G     1
                                     
                                        1I
                                         J     0.0041
                 0.0001256
                           H    16 14    K
           Reject Ho. There mean team batting average is different for the American and national
           League teams..
      c.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
                 (16  1)(0.826)  (14  1)(0.833)
                                    2                   2
            s2                                            0.6877
                               16  14  2
             p

                   2.402  2.299             .
                                            0103
            t                                     0.339
                          F
                          G1
                               
                                    1I
                                     J     0.3035
                 0.6877
                          H
                          16 14      K
           Do not reject Ho. There is no difference in the mean attendance between National and
           American League teams.
      d.   Ho: T = G                    H1: T  G               Reject Ho if t > 2.048 or t < 2.048
                 (21  1)(318)  (9  1)(47.0)
                             .    2                 2
            s2                                        1353.46
                            21  9  2
             p

                   1761  1517
                       .        .            24.4
            t                                      1.665
                          F I
                          G J
                            1 1
                                
                                           14.6572
                 1353.46
                          H K
                           21 9
           Do not reject Ho. There is no difference between the mean number of home runs hit by
           teams with artificial turf stadiums and those with grass fields


                                                 93                                   Chapter 9
51.     Ho: 1 = 2               H1: 1  2            Reject Ho if t > 2.052 or t < 2.052
             (22  1)(354)  (7  1)(150)
                       .   2
                                         . 2
        s2                                   10.2468
                        22  7  2
         p

               12.89  14.59       17000
                                       .
        t                                  1224
                                                .
                     F I
                     G J 1 1
                          
                                     .
                                    13891
             10.2468
                     H K
                       22 7
        Do not reject Ho. There is no difference in the mean percent of the population over 65 years of
        age for G7 countries and non G7 countries.




Chapter 9                                          94

								
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