We wish to estimate the differenceABin mean fuel efficiencies for twobrands of automobile. We measure the fuel efficiencies (in mpg)of samples of cars for each brand. The data are shown below with some summary statistics:

Brand A 40.7 43.8 36.5 38.4 45.0 37.6 41.2 mean = 40.46 std. dev. = 3.17 Brand B 37.4 33.9 40.1 38.9 36.2 mean = 37.30 std. dev. = 2.41

Assume that fuel efficiencies are known to follow normal distributions for both brands. (a) What is the estimate of the common variance of fuel efficiencies for the two brands of automobile?(Round your answer tothreedecimal places.) (b)Calculate a99% confidence interval for the difference in the mean fuel efficiency forthe two brands of automobile.

We would like to conduct a test ofH0:A=Bvs.Ha:ABat the 1% level of significance to determine whether the true mean fuel efficiency for Brand A is different than that for Brand B. (c) What is the value of the test statistic for the appropriate test of significance? (d) What is the P-value of the test? (e) What is the correct conclusion of the test? (f) Suppose we had instead conducted the test using an analysis of variance. What would be the value of the test statistic and the P-value?

(g)Verify your results by conducting theappropriate hypothesis test inJMP. To do this, create a column calledFuel Efficiencyand enter all 12 data values in this column (all7 data values for Brand Aand then all5 data values for Brand B). Create a second column calledBrandand typeAin the first7 rows (beside the data values for the Brand A cars) andBin the next5 rows (beside the data values for the Brand B cars). Go toAnalyze > Fit Y by X. ChooseFuel Efficiencyas Y andBrandas X. ClickOK. Now, if you want to conduct a pooled two-sample t test, under the red arrow, selectMeans, Anova, Pooled t. If you want to conduct a conservative (unpooled) two sample t test, under the red arrow, selectt Test.

What is the exact P-value of the test?

(h) Suppose we had instead used the critical value method to conduct the test. What would be the decision rule and the conclusion?