The manufacturer of Boston and Vermont asphalt shingles provides its customers with a 20-year warranty on most of its products. To determine whether a shingle will last through the 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 in a laboratory setting via an 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. The file Grantule 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, is there evidence at the 0.05 level of significance that the population mean granule loss is different from 0.30 grams?
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 granule loss is different from 0.30 grams?
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.