A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.03 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.968 gallon.

a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.

b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company? Why?

Yes,

No,

because a 1-gallon bottle containing exactly 1-gallon of water lies outside or within the 99% confidence interval.

outside

within

c. Must you assume that the population amount of water per bottle is normally distributed here? Explain.

D. Construct a 90% confidence interval estimate. How does this change your answer to part (b)