Chapter 8.6, Problem 50E

Refer to Example 8.8. In this example, p₁ and p₂ were used to denote the proportions of refrigerators of brands A and B, respectively, that failed during the guarantee periods.

a At the approximate 98% confidence level, what is the largest “believable value” for the difference in the proportions of failures for refrigerators of brands A and B?

b At the approximate 98% confidence level, what is the smallest “believable value” for the difference in the proportions of failures for refrigerators of brands A and B?

c If p₁ − p₂ actually equals 0.2251, which brand has the larger proportion of failures during the warranty period? How much larger?

d If p₁ − p₂ actually equals −0.1451, which brand has the larger proportion of failures during the warranty period larger? How much larger?

e As observed in Example 8.8, zero is a believable value of the difference. Would you conclude that there is evidence of a difference in the proportions of failures (within the warranty period) for the two brands of refrigerators? Why?