A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found to be 16.5, and the sample standard deviation, s, is found to be 5.8. (a) Construct a 96% confidence interval about mu if the sample size, n, is 37. (b) Construct a 96% confidence interval about mu if the sample size, n, is 52. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about mu if the sample size, n, is 37. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval? Question content area bottom Part 1 (a) Construct a 96% confidence interval about mu if the sample size, n, is 37. Lower bound: 14.47; Upper bound: 18.53 (Round to two decimal places as needed.) Part 2 (b) Construct a 96% confidence interval about mu if the sample size, n, is 52. Lower bound: 14.80; Upper bound: 18.20 (Round to two decimal places as needed.) Part 3 How does increasing the sample size affect the margin of error, E? A. The margin of error decreases. This is the correct answer.B. The margin of error increases. Your answer is not correct.C. The margin of error does not change. Part 4 (c) Construct a 98% confidence interval about mu if the sample size, n, is 37. Lower bound: 13.40; Upper bound: 16.60 (Round to two decimal pl