Question

Super Sneaker Company is evaluating two different materials, A and B, to be used to construct the soles of their new active shoe targeted to city high school students in Canada. While material B costs less than material A, the company suspects that mean wear for material B is greater than mean wear for material A. Two study designs were initially developed to test this suspicion. In both designs, Halifax was chosen as a representative city of the targeted market. In Study Design 1, 15 high school students were drawn at random from the Halifax School District database. After obtaining their shoe sizes, the company manufactured 15 pairs of shoes, each pair with one shoe having a sole constructed from material A and the other shoe, a sole constructed from material B.

After 3 months, the amount of wear in each shoe was recorded in standardized units as follows:

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
A	12.43	9.34	7.88	10.78	8.54	8.29	9.73	9.61	11.61	8.08	8.77	12.08	9.98	9.37	11.51
B	10.95	11.28	10.21	9.73	11.54	10.48	9.45	10.84	10.81	10.04	9.18	8.52	12.73	9.94	10.16

For this question, I would like help calculating the SA and SB - components of the test statistic - by hand. The SA I got was 1.7857x10^(-8), but I feel like that's incorrect.

Answer 1

From the given data

H0: The Mean wear for Material B is not greater than mean wear for material A

H1; The Mean wear for Material B is greater than mean wear for material A

Let the los be alpha = 0.05

From the above table

Thus we conclude that the Mean wear for Material B is not greater than mean wear for material A