A car manufacturer claims that one of their models, let’s call it Mendel A, on a

Question

A car manufacturer claims that one of their models, let’s call it Mendel A, on average has a significantly shorter stopping distance than a competition’s model, let’s call it Model B, in the same class. To test their claim the distance (in feet) it took for 8 Model A cars to get to complete stop from 60 miles per hour was recorder. The same was done for 9 Model B cars. The result were as follows.

Model A: 98, 97, 99, 101, 95, 99, 100, 95 Model B: 94, 101, 100, 102, 100, 99, 97, 102, 96

(A) [3] Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or unequal? Explain.

(B) At 5% level of significance is there sufficient evidence to indicate that the claim of the manufacturer of Model A is true? Use the critical value approach.

(C) [2] What is the p-value for the test in (B)?

(D) [1] Is it necessary to assume that the populations are normally distributed to validate the test in (B)?

Explanation / Answer

A) Compute the variances for Model A and Model B. VarianceA=4.857, VarinceB=7.750

Ratio of variances=4.857/7.750=0.627. The value indicates that population variances are not unequal.

B) Using nA=8-1=7 and nB=9-1=8, the critical regio of F test statistic is 3.73. The test statistic do not fall in critical region. Fail to reject null hypothesis.

C) P value for the test is 0.665.

d) Population are normally distributed.

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