4. Julie visits the local park 90 times, and sees her favoritepigeon 38 times. Let p be the probability that Julie sees thepigeon on any given visit, and assume that whether Julie sees thepigeon on some visit is independent of whether she sees the pigeonon any other visit.
(a) Construct a 90% two-sided confidence interval for p.
(b) Julie believes that there is a 50% chance that she sees thepigeon when she visits the park. Is your interval in part (a)consistent with that belief? Explain your answer.
(c) Test Julie’s claim from part (b) with a hypothesis test. Usea significance level of α = 0.05. Perform the test by comparing atest statistic to a critical value found in the tables in the backof your textbook.
(d) Perform the test in part (c) using a p-value.
