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, 8 high school students were drawn at random from the Halifax School District database. After obtaining their shoe sizes, the company manufactured 8 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
A	17.23	13.09	11.13	15.02	12.01	11.68	13.62	13.45
B	14.73	15.17	13.73	13.08	15.51	14.09	12.70	14.57

What is the 99% confidence interval for the difference in wear between material B and material A (use B-A)? Use software to get a more precise critical value, but confirm it's roughtly the same value you get from the table. Use at least 5 digits to the right of the decimal. Lower bound:  Upper bound:

Alternative hypothesis was: uA-uB < 0

Answer 1

from software critical value of t= 3.49948 which is approximately the same from table which is 3.499

for 99% CI; and 7 degree of freedom, value of t=			3.49948
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		2.81433
lower confidence limit                     =		-2.02058
upper confidence limit                    =		3.60808

lower bound =-2.02058

upper bound =3.60808