Question

A shoe company designed a low-top and high-top version of a particular shoe. One of the shoe-making engineers claims that the low-top version does not last as long as the high-top version before wearing out. To test this claim, she takes a sample of 36 low-top and 64 high-top wearers and asks each the length of time before their shoes wore out. She finds that the low-tops wore out in an average of 140 days, and the high-tops wore out in an average of 150 days. Suppose the population standard deviation for both is 20 days.

a. Specify the competing hypotheses to determine whether high-tops last longer than low-tops for this particular shoe.

b. Calculate the value of the relevant test statistic.

c. Compute the p-value. Does the evidence support the commentator’s claim at the 1% significance level?

Answer 1

X1 bar	150		X2 bar	140
S1	20		S2	20
n1	64		n2	36

a)

Hypothesis:

H0: μ1 <= μ2

Ha: μ1 > μ2

alpha = 0.01

b)

Test:

Z stat = (X1 bar-X2 bar )/SQRT(S1^2/n+S2^2/n) = (150-140)/SQRT(20^2/64+20^2/36) = 2.4

c)

P value = 0.0082 (From Z table)

d)

P value < 0.01, Reject H0

There is enough evidence to conclude that high-tops last longer than lowtops for this particular shoe at 1% significance level