A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 18.2, and the sample standard deviation, s, is found to be 5.7 (a) Construct a 95% confidence interval about u if the sample size, n, is 39. (b) Construct a 95% confidence interval about u if the sample size, n, is 57. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 14, what conditions must be satisfied to compute the confidence interval? (c) Construct a 98% confidence interval about u if the sample size, n, is 39 Lower bound: 15.90 , Upper bound: 20.43 (Round to two decimal places as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error does not change. O B. The margin of error increases O C. The margin of error decreases (d) If the sample size is 14, what conditions must be satisfied to compute the confidence interval? Q A. The sample data must come from a population that is normally distributed with no outliers. B. Since the sample size is suitably large, the population need not be normally distributed, but it still should not contain any outliers O C. The sample must come from a population that is normally distributed and the sample size must be large. More