Chapter 8, Problem 9PS

A bottled water distributor wants to estimate the amount of water contained in -gallon bottles purchased from a nationally known water botting company. The water botting company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 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 botting company about the amount of water that the bottles contain? Why?

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

d. Construct a 95% confidence interval estimate. How doe this change your answer to (b)?