Question

Are women's feet getting bigger? Retailers in the last 20 years have had to increase their stock of larger sizes. Wal-Mart Stores, Inc., and Payless ShoeSource, Inc., have been aggressive in stocking larger sizes, and Nordstrom's reports that its larger sizes typically sell out first. Twelve women from each age group were randomly selected and their shoe sizes recorded. Use α = .05.

Born in 1980 Born in 1960

8.0 8.5

7.5 7.5

8.5 8.0

8.5 8.0

8.0 7.5

7.5 7.5

9.5 7.5

7.5 8.0

8.0 7.0

8.0 8.0

8.5   7.0

9.0 8.0

a. First test to determine if the variances in women’s shoe sizes differ between years. Show and follow the 7 steps for hypothesis testing.

b. What assumption is required to test for equality of variances? Construct an appropriate graph(s) using Minitab and explicitly answer if the assumption is valid or not.

c. Verify your results in part (a) using Minitab.

d. Using the information from your results in part (a), test to determine if average women’s shoe sizes have increased. Follow and show the 7 steps for hypothesis testing.

e. Verify your results in part (c) using Minitab.

Step 1: State the research question or objective.

Step 2: Formulate the null and alternative hypotheses.

Step 3: Choose a significance level.

Step 4: Determine the appropriate test statistic and its distribution. State the Decision Rule.

Step 5: Calculate the test statistic and its p-value

Step 6: Decision. Using the Decision Rule, compare p-value to a and make a decision.

Step 7: Written Conclusion. Compare the decision to the hypotheses and write the conclusion.

Answer 1