A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample mean, x, is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9.

(a) Construct the 90% confidence interval for the population mean if the sample size, n, is 15.

(b) Construct the 90% confidence interval for the population mean if the sample size, n, is 25.How does increasing the sample size affect the width of the interval?

(c) Construct the 95% confidence interval for the population mean if the sample size, n, is 15. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the confidence interval?