everage annual repair cost for an automobile depends on the age of the automobil

Question

everage annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in tinding out whether 2 sample standard deviation for annual repair costs of $118.75. Let 4 year old automobiles be represented by the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a s ·The data is located in the Microsoft Excel Orine file below 2. Conduct the hypothesis test at a 0.05 level of significance Calculate the value of the test statistic [2 decimals). o e Type here to search PrtScn 7 9 0

Explanation / Answer

Test and CI for Two Variances: C1, C2

Method

Null hypothesis         (C1) / (C2) = 1
Alternative hypothesis (C1) / (C2) > 1
Significance level      = 0.05

F method was used. This method is accurate for normal data only.

Statistics

                                  95% Lower
                                  Bound for
Variable   N    StDev   Variance     StDevs
C1        26 171.524 29420.566    139.765
C2        23 118.751 14101.719     95.629

Ratio of standard deviations = 1.444
Ratio of variances = 2.086

95% One-Sided Confidence Intervals

        Lower Bound   Lower Bound
          for StDev for Variance
Method        Ratio         Ratio
F             1.016         1.033

Tests

                       Test
Method DF1 DF2 Statistic P-Value
F      25   22       2.09   0.043

1)
Ho: sigma^2_1 = sigma^2_2
Ha: sigma^2_1 >= sigma^2_2

2)
TS = 2.09
critical value =

p-value = 0.043
yes , reject the null
there is significant evidence that that variance in annual repair costs is larger than the older

2.019644

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