Please show calculations

I . . . 1. Let's again revisit the study about spam emails. We collected a (suitably) random sample of 1422 emails, and we set the probability of receiving a spam email, the probability of getting a "success," at p = 0.85. Say our sample had 1137 successes. a. What are the values of p and q for this sample? b. What is the standard deviation of the best point estimate for this sample? c. What are the multipliers for a 90%, 95%, and 99% confidence interval, respectively? d. Compute the 90%, 95%, and 99% confidence intervals for the proportion of successes. e. Write a sentence that summarizes the information conveyed by the 95% confidence interval. 2. On a previous quiz we discussed a study about people's preferences for Coke or Pepsi. We surveyed 200 people, counted a vote for Coke over Pepsi as a success, a chose as our null hypothesis Ho: p = 0.63. Let's say our sample saw 147 successes. a. Compute a 95% confidence interval for the true proportion according to this survey. b. Does this 95% confidence interval contain the hypothesized value of p? Justify your answer. c. Compute a 92% confidence interval according to the survey. (Hint: use the Normal distribution utility (or Google) to find the multiplier for 92%). a. For the spam emails study, assume that the null hypothesis is Ho: p = 0.85 and the research hypothesis is H,:p