Running Shoes. A shoe designer tests a new material for the soles of their most popular line of running shoes. She has 7 athletes run 100 miles with one of last years shoes and one of these new shoes, randomly assigning the new shoe to the left or right foot. Afterward, she measures the amount of wear on each of the shoes in millimeters. Test the claim that the amount of wear with the new material is different from the amount of wear with the old material.

Runner	1	2	3	4	5	6	7
New Material Wear	1.09	1.06	1.13	1.08	1.14	1.08	1.1
Old Material Wear	1.01	0.97	1.12	1.01	0.98	0.95	0.96

(a) Why are these paired data?

• Each runner has a pair of shoes.
• This table does not have paired data; there is no clear relationship between the top and bottom values in any column.
• Runners typically run in groups of two.
• There are an equal number of shoes of each type.
• The top and bottom values in each column are from the same runner.

(b) Write the hypotheses in symbols.

• H_o: _diff=new-old = 0 H_a: _diff=new-old > 0
• H_o: _diff=new-old = 0 H_a: _diff=new-old 0
• H_o: _diff=new-old = 0 H_a: _diff=new-old < 0

(c) Put the list of differences in your calculator and use T-Test to find the p-value. p = (please round to three significant figures) (d) What is the conclusion of the hypothesis test?

• Since p 0.05 we support the null hypothesis.
• Since p < 0.05 we reject the null hypothesis and support the alternative.
• Since p 0.05 we fail to reject the null hypothesis.
• Since p 0.05 we reject the null hypothesis and support the alternative.
• Since p < 0.05 we fail to reject the null hypothesis.

(e) What is the final conclusion in everyday language?

• There is not sufficient evidence to reject the claim that the wear amounts are different.
• There is not sufficient evidence to support the claim that the wear amounts are different.
• There is sufficient evidence to support the claim that the wear amounts are different.
• There is sufficient evidence to reject the claim that the wear amounts are different.