A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 50, and the sample standard deviation,s, is found to be 8.

(a) Construct a 98% confidence interval for µ if the sample size, n, is 20.

(b) Construct a 98% confidence interval for µ if the sample size, n, is 15. How does decreasing the sample size affect the margin of error, E?

(c) Construct a 95% confidence interval for µ if the sample size, n, is 20. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the margin of error, E?

(d) Could we have computed the confidence intervals in parts (a)–(c) if the population had not been normally distributed? Why?