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 as long as the warranty period, accelerated-life testing is conducted at the manufacturing plant. Accelerated- life testing exposes a shingle to the stresses it would be subject to in a lifetime of normal use via an experiment in a laboratory setting 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 gram 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. List the five-number summaries for the Boston shingles and for the Vermont shingles.
b. Construct side-by-side boxplots for the two brands of shingles and describe the shapes of the distributions.
c. Comment on the ability of each type of shingle to achieve a granule loss of 0.8 gram or less.