Question: Studies conducted by a manufacturer of “Boston” and “Vermont” asphalt shingles have shown product weight to be a major factor in the customer’s perception of quality. Moreover, the weight represents the amount of raw materials being used and is therefore very important to the company from a cost standpoint. The last state of the assembly line packages the shingles before the packages are placed on wooden pallets. Once a pallet is full (a pallet for most brands holds 16 squares of shingles), it is weighed and the measurement is recorded. The data file PALLET contains the weight in pounds from a sample of 368 pallets of Boston shingles and 330 pallets of Vermont shingles.

a) For the Boston shingles, is there evidence that the mean weight is different from 3,150 pounds?

Perform the test using both a test statistic/tabulated critical value approach and a p-value approach. Your solution should begin with a statement of the hypothesis, and then show the decision rule(s) and the application of that decision rule to reach a conclusion. It should end with an interpretation of the conclusion in the context of the problem.