Posted: August 2nd, 2022

Statistic Problems

4 problems to be completed.

Problem 9.76

9.76 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 mois-ture 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.

Problem 9.77

9.77 Studies conducted by the manufacturer of Boston and Vermont asphalt shingles have shown product weight to be 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 the packages 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.
a. For the Boston shingles, is there evidence at the 0.05 level of significance that the population mean weight is different from 3,150 pounds?
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 weight is different from 3,700 pounds?
d. Interpret the meaning of the p-value in (c).
e. In (a) through (d), do you have to be concerned with the normal-ity assumption? Explain

Problem 9.78

9.78 The manufacturer of Boston and Vermont asphalt shingles provides its customers with a 20-year warranty on most of its prod-ucts. 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 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, 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 normal-ity assumption? Explain

Problem 9.79

9.79 Referring to the results of Problems 9.76 through 9.78 concerning Boston and Vermont shingles, write a report that evaluates the moisture level, weight, and granule loss of the two types of
shingles

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