A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as eight ounces, the company wants the packages to contain a...

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as eight ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than eight ounces. A sample of 50 packages is selected periodically and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.162 ounces, with a sample standard deviation of 0.052 ounce.

a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.01 level of significance.)

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