A simple random sample of size n is drawn. The sample mean, x, is found to be 18.4, and the sample standard deviation,s, is found to be 4.5.

(a) Construct a 95% confidence interval for µ if the sample size, n, is 35.

(b) Construct a 95% confidence interval for µ if the sample size, n, is 50. How does increasing the sample size affect the margin of error, E?

(c) Construct a 99% confidence interval for µ if the sample size, n, is 35. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the margin of error, E?

(d) If the sample size is n = 15, what conditions must be satisfied to compute the confidence interval?