5. Suppose that a random sample of n = 150 U.S. adults shows that X = 87 of them wear corrective lenses. Find a 95% confidence interval for p, the actual proportion of U.S. adults who wear corrective lenses. (For this question, assume that p is not actually known. Show your work.)

6. Suppose again that it is known that 60% of all U.S. adults wear corrective lenses. A researcher suspects that the proportion of adults living in Hawaii who wear corrective lenses is lower than 60%. She plans to run a hypothesis test using a random sample of n = 250 Hawaiian adults.

a) If p is the actual proportion of Hawaiian adults who wear corrective lenses, what are the appropriate null and alternative hypotheses for this test? (You may write your answers in words or symbols, but label your answers clearly.)

b) Without referring to the actual sample information provided in part (c), describe in words or using symbols what would lead the researcher to reject the null hypothesis in favor of the alternative hypothesis. (Assume she will use a significance level of = .05. Be as precise as possible, using the standard normal variable Z if appropriate.)

c) Now suppose that the random sample of 250 Hawaiian adults shows that 139 of them wear corrective lenses of some type. How should the researcher report her findings?

d) If the researcher also reports a P -value for this test, what is that value? Describe in words what this value means.