An important quality characteristic used by the manufacturer of Boston and Vermont asphalt shingles is the amount of moisture the shingles contain when they are packaged. Customers may feel that they have purchased a product lacking in quality if they find moisture and wet shingles inside the packaging. In some cases, excessive moisture can cause the granules attached to the shingles for texture and coloring purposes to fall off the shingles, resulting in appearance problems. To monitor the amount of moisture present, the company conducts moisture tests. A shingle is weighed and then dried. The shingle is then reweighed, and, based on the amount of moisture taken out of the product, the pounds of moisture per 100 square feet are calculated. The company would like to show that the mean moisture content is less than 0.35 pound per 100 square feet. The file moisture includes 36 measurements (in pounds per 100 square feet) for Boston shingles and 31 for Vermont shingles.
a. For the Boston shingles, is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet?
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 moisture content is less than 0.35 pound per 100 square feet?
d. Interpret the meaning of the p-value in (c).
e. What assumption about the population distribution is needed in order to conduct the t tests in (a) and (c)?
f. Construct histograms, boxplots, or normal probability plots to evaluate the assumption made in (a) and (c).
g. Do you think that the assumption needed in order to conduct the t tests in (a) and (c) is valid? Explain.