Hypothesis Testing: z-tests. Beauty Lotion is a skin-moisturizing product that contains rich oils, blended especially for overly dry or neglected skin. The product is sold in 5-ounce bottles by a wide range of retail outlets. In an ongoing review of product quality and consistency, the manufacturer of Beauty Lotion found a sample average product volume of 5.2 ounces per unit with a sample standard deviation of 0.12 ounces, when a sample of n = 144 observations was studied.

A. Calculate the range within which the population average volume can be found with 99 percent confidence.

B. Assuming that s = 0.12 cannot be reduced, and a sample size of n = 144, what is the minimum range within which the sample average volume must be found to justify with 99 percent confidence the advertised volume of 5 ounces?