Studies conducted by the 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 stage 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 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 at the 0.05 level of significance that the population mean weight is different from 3,150 pounds?
b. Interpret the meaning of the p-value in (a).
c. For the Vermont shingles, is there evidence at the 0.05 level of significance that the population mean weight is different from 3,700 pounds?
d. Interpret the meaning of the p-value in (c).
e. In (a) through (d), do you have to be concerned with the normality assumption? Explain.