Chapter 9.2, Problem 17AYU

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, $\bar{x}$, is found to be 108, and the sample standard deviation, s, is found to be 10.

1. a. Construct a 96% confidence μ interval for p if the sample size, n, is 25.
2. b. Construct a 96% confidence μ interval for p if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E?
3. c. Construct a 90% confidence μ interval for p if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?
4. d. Could we have computed the confidence intervals in parts (a)–(c) if the population had not been normally distributed? Why?