In Example 7.9 we stated that the Hartley test was not appropriate because there was evi...

In Example 7.9 we stated that the Hartley test was not appropriate because there was evidence that two of the population distributions were non normal. The BFL test was then applied to the data and it was determined that the data did not support a difference in the population variances at an α = .05 level. The data yielded the following summary statistics:

a. Using the plots in Example 7.9, justify that the population distributions are not normal.

b. Use the Hartley test to test for differences in the population variances.

c. Are the results of the Hartley test consistent with those of the BFL test?

d. Which test is more appropriate for this data set? Justify your answer.

e. Which of the additives appears to be a better product? Justify your answer.

REFERENCE:

EXAMPLE 7.9

Three different additives that are marketed for increasing the miles per gallon (mpg) for automobiles were evaluated by a consumer testing agency. Past studies have shown an average increase of 8% in mpg for economy automobiles after using the product for 250 miles. The testing agency wants to evaluate the variability in the increase in mileage over a variety of brands of cars within the economy class. The agency randomly selected 30 economy cars of similar age, number of miles on their odometer, and overall condition of the power train to be used in the study. It then randomly assigned 10 cars to each additive. The percentage increase in mpg obtained by each car was recorded for a 250-mile test drive. The testing agency wanted to evaluate whether there was a difference between the three additives with respect to their variability in the increase in mpg. The data are give here along with the intermediate calculations needed to compute the BFL’s test statistic.

Solution Using the plots in Figures 7.12(a)–(d), we can observe that the samples from additive 1 and additive 2 do not appear to be samples from normally distributed