Question

Begin by re-writing the problem. Minitab18 is required; attach or include your output. Type (use Word) your assignment; you may handwrite equations.

1) 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.  The data are shown below and may be found in the data filed named ShoeSize1.Use α = .05. 25 points.

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. (8 points)
• 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. (5 points)
• c) Verify your results in part (a) using Minitab. (2 points)
• 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. (8 points)
• e) Verify your results in part (c) using Minitab. (2 points)

Answer 1

b) Construct an appropriate graph(s) using Minitab and explicitly answer if the assumption is valid or not. (5 points)

Ans:

From the above graphs and p-values, we can conclude that both the data follow the normal distributions.

c) Verify your results in part (a) using Minitab. (2 points)

Ans:

It has similar p-value as in (a). So, the same conclusion.

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

It has similar p-value as in (d). So, the same conclusion.