The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually is 1 gallon. It is known from the manufacturer's specifications that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon can is found to be .995 gallon.
a. Is there evidence that the mean amount is different from 1.0 gallon (use a=0.01)?
b. Compare the p-value and interpret its meaning.
c. Construct a 99% confidence interval estimate of the population mean amount of paint.
d. Compare the results of (a) and (c). What conclusions do you reach?