Please solve question 3. I posted Question 1 for reference to 3a.

3. In a survey of 400 likely voters, 215 responded that they would vote for the incumbent, and 185 responded that they would vote for the challenger. Let p the denote the fraction of all likely voters Who preferred the incumbent. (a Compute 13 from Question 1 using the survey data. ( b (c (d What is the p-value for the test of H0 : p = 0.5 versus H1 : p > 0.5? Compute the standard error of :3. What is the pvalue for the test of H0 : p = 0.5 versus H1 : 19 # 0.5? ) ) ) ) (e) Why do the results from (c) and (d) differ? (f) Did the survey contain statistically significant evidence that the incumbent was ahead at the time of the survey? (g) Construct a 95% confidence interval for p. (h) Construct a 99% confidence interval for p. (i) Why is the 99% confidence interval wider than the 95% confidence interval? (j) Without doing any additional calculations, use the results from parts (g) and (h) to test the hypothesis Ho : p = 0.6 vs H1 : p # 0.6 at a 5% and 1% significance level.1. Let Y be a Bernoulli random variable with success probability P(Y = 1) = p. Let Y1, Y2, ..., Yn be and i.i.d sample from this distribution. Let n p 1 {Yi = 1} . n :1 (a) Show that p is an unbiased estimator of p. (b) Show that Varlp] = P(1-p) n