The manufacturer of Boston and Vermont asphalt shingles provides its customers with a 20year warranty on most of its products. To determine whether a shingle will last the entire warranty period, accelerated life testing is conducted at the manufacturing plant. Accelerated life testing exposes the shingle to the stresses it would be subject to in a lifetime of normal use via a laboratory experiment that takes only a few minutes to conduct. In this test, a shingle is repeatedly scraped with a brush for a short period of time, and the shingle granules removed by the brushing are weighed (in grams). Shingles that experience low amounts of granule loss are expected to last longer in normal use than shingles that experience high amounts of granule loss. In this situation, a shingle should experience no more than 0.8 grams of granule loss if it is expected to last the length of the warranty period. The file Granule contains a sample of 170 measurements made on the company's Boston shingles and 140 measurements made on Vermont shingles.
a. For the Boston shingles, construct a 95% confidence interval estimate for the mean granule loss.
b. For the Vermont shingles, construct a 95% confidence interval estimate for the mean granule loss.
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 granule loss of the Boston and Vermont shingles?