Assignment

1. A nylon rope maker claims its repelling rope's average breaking strength is at least 800 pounds. A researcher sets up a hypothesis test regarding the breaking strength of the rope where Ho: μ ≤ 800. where α = .05.

a. Rewrite his null and alternative hypotheses as complete sentences. What does the hypothesis suggest about where the benefit of the doubt is being placed? Explain your answer.

b. What does it mean to make a type I error, and, specifically, what would constitute a type one error in this case?

c. In this case, is it appropriate to use α = .05? Explain why or why not.

d. What would we conclude if the sample average was much larger than 800 pounds?

e. What would we conclude if the sample average was slightly less than 800 pounds?

f. What if the sample average is much less than 800?

2. Pennsylvania Governor Tom Ridge has a longstanding reputation for being "tough on crime." His opponent is currently running ads that dispute this. Before Ridge took office, the average criminal spent 12.5 years in prison before parole. Ridge's opponent says that a random sample of forty-nine recent parolees spent an average of only eleven years in prison (the standard deviation in the sample was fourteen years). Assuming you work for an independent newspaper, evaluate the claim made by the Ridge opponent. What would you report to your readers? Test at the 05 percent level of significance.

3. Using the last problem calculate the 95 percent confidence interval. Interpret this interval.