Question

The ACME Fuel Company is testing three gasoline additives that potentially improve miles per gallon (mpg). Data on the mpg increases are listed below.

(a) For each of the three additives, make boxplots, probability plots, run Anderson-Darling tests, and Shapiro-Wilks tests to check for normality.

(b) Based the results in part (a), which test (Hartley’s F-max, Bartlett’s, Levene’s) is best to use to check for a difference between the variances of mpg increases for the three additives?

(c) Run the test you suggested in part (b). Be sure to state the null and alternative hypotheses, test statistic, p-value, and conclusion.

Additive 1 Additive 2 Additive 3
6.549242425   10.82721186   16.39651385
8.60769443 8.672993094   13.82644019
5.053919216   8.212382471 6.331782807
2.967964673   11.08228374   10.45064681
7.978100632   8.590190877   21.82354105
7.463924823   10.55720623   10.28018859
10.53623928   9.740637014   15.88060475
9.289187964   7.707613874   13.74817698
5.115349588   10.3504957    10.60781807
8.688854234   9.293838784   10.84792601

Answer 1

(a) The boxplot is:

The probability plots are:

For Additive 1:

For Additive 2:

For Additive 3:

The normality test results are:

(b) The best test to use to check for a difference between the variances of mpg increases for the three additives is Hartley’s F-max test.

(c) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H₁: At least one means is not equal

The SPSS output is:

The test statistic is 10.096.

The p-value is 0.001.

Therefore, we can conclude that there is a difference between the variances of mpg increases for the three additives.