The manufacturer of Boston and Vermont asphalt shingles knows that product weight is a major factor in a customer's perception of quality. The last stage of the assembly line packages the shingles before they 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 |2B1 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, construct a 95% confidence interval estimate for the mean weight.
b. For the Vermont shingles, construct a 95% confidence interval estimate for the mean weight.
c. Do you think the assumption needed to construct the confidence interval estimates in (a) and (b) is valid?
d. Based on the results of (a) and (b), what conclusions can you reach concerning the mean weight of the Boston and Vermont shingles?