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The manufacturer of Boston and Vermont asphalt shingles knows that product weight is 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 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 Pallet contains the weight (in pounds) from a sample of 368 pallets of Boston shingles and 330 pallets of Vermont shingles.
Completely analyze the differences in the weights of the Boston and Vermont shingles, using a = 0.05.

Is there sufficient evidence to
conclude that the mean weights of Boston and Vermont shingles are different?

answer the question, and provide
a comprehensive explanation.