Chapter 9, Problem 16PS

A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water botting company is actually 1 gallon. You know from the water botting 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 of water per 1-gallon is 0.995 gallon.

a. Is there evidence that the mean amount is different from 1.0 gallon? $\text{(Use}\alpha =\mathrm{0.01.})$

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?