9.16 A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water per bottle is 0.02 gallon. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle is 0.995 gallon.

a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a = 0.01.)

b. Compute the p-value and interpret its meaning.

c. Construct a 99% confidence interval estimate of the population mean amount of water per bottle.

d. Compare the results of (a) and (c). What conclusions do you reach?