Please show me how to solve these problems

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 Compute p and q for this sample. b. Compute 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 H : 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%%). 3 a. In the context of the spam emails study, what would constitute a Type I enor? What would constitute a Type II error? b. Let's say this study was being conducted to determine how a company is going to design a spam filter. What do you think would be the possible consequences of a Type I enor? What would be the possible consequences of a Type II error? Discuss in detail. a. In the context of the Coke and Pepsi study, what would constitute a Type I error? What would constitute a Type II error? b Let's say that either Coke or Pepsi was going to use the results of this study to alter their marketing strategy. What do you think would be the possible consequences of a Type I error? What would be the possible consequences of a Type II error? Discuss in detail