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					Insurance adjusters are concerned about the high estimates they are receiving from two garages.
Cars were taken to both garages and the estimates (in hundreds of dollars) are recorded below.
               Car Garage 1 Garage 2
                 1        17.6      17.3
                 2        20.2      19.1            25
                 3        19.5      18.4
                 4        11.3      11.5
                 5          13      12.7            20
                 6        16.3      15.8
                 7        15.3      14.9
                 8        16.2      15.3            15
                 9        12.2        12
                10        14.8      14.2            10         Garage 1               Garage 2
                11        21.3        21
                12        22.1        21
                13        16.9      16.1              5
                14        17.6      16.7
                15        18.4      17.5
             mean 16.84667 16.23333                   0
                sd 3.203986 2.94125

t-Test: Two-Sample Assuming Unequal Variances       Ho: mu1 =mu2           Ha: mu1 NOT = mu2

                    Garage 1 Garage 2            t= (16.85-16.23)-0                 = 0.62/1.12
Mean                 16.84667 16.23333              sqrt(3.2^2/15+2.94^2/15)          0.55
Variance             10.26552 8.650952
Observations               15       15
Hypothesized Mean Difference0                       The t is very close to 0, and using a computer, we get a
df                         28                       pv=0.29.We fail to reject and conclude we couldn't find a
t Stat               0.546163                       difference in the two garages.
P(T<=t) one-tail      0.29464
t Critical one-tail   1.70113
P(T<=t) two-tail      0.58928
t Critical two-tail  2.048409

t-Test: Two-Sample Assuming Equal Variances

                    Garage 1 Garage 2
Mean                 16.84667 16.23333
Variance             10.26552 8.650952
Observations               15       15
Pooled Variance      9.458238
Hypothesized Mean Difference0
df                         28
t Stat               0.546163
P(T<=t) one-tail      0.29464
t Critical one-tail   1.70113
P(T<=t) two-tail      0.58928
t Critical two-tail  2.048409
ouldn't find a
          Car Garage 1 Garage 2 Difference
            1      17.6     17.3        0.3
            2      20.2     19.1        1.1
            3      19.5     18.4        1.1       1.2
            4      11.3     11.5       -0.2
            5        13     12.7        0.3         1
            6      16.3     15.8        0.5
            7      15.3     14.9        0.4       0.8
            8      16.2     15.3        0.9       0.6
            9      12.2       12        0.2
           10      14.8     14.2        0.6       0.4
           11      21.3       21        0.3
           12      22.1       21        1.1       0.2
           13      16.9     16.1        0.8
                                                    0
           14      17.6     16.7        0.9
           15      18.4     17.5        0.9      -0.2
         mean 16.84667 16.23333 0.613333                                    Differenc
           sd 3.203986 2.94125 0.394365          -0.4                           e

t-Test: Paired Two Sample for Means

                   Garage 1 Garage 2     t= 0.61-0                 = 6.06         pv=0, it's off the chart
Mean                16.84667 16.23333       0.39/sqrt(15)
Variance            10.26552 8.650952
Observations              15       15         Now, we see that there really IS a difference in the
Pearson Correlation 0.995411                  two shops estimates!
                           0
Hypothesized Mean Difference
df                        14
t Stat              6.023428
P(T<=t) one-tail 1.56E-05
t Critical one-tail 1.761309
P(T<=t) two-tail 3.13E-05
t Critical two-tail 2.144789

				
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posted:10/5/2011
language:English
pages:4