Question

9.76 An important quality characteristic used by the manufac- turer 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 mois- ture 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 moisture per 100 square feet are calculated. The company wo like to show that the mean moisture content is less than 0.35 pou per 100 square feet. The file Moisture includes 36 measuren

Just need letter A and C done. Thank you!!

Answer 1

a )

There is no data given in the question , hence i shall simulate some and show how to run the analysis in excel

The hypothesis can be constructed as

H0 : There is no evidence at 0.05 level that the population moisture content is less than 0.35
H1 : There is signficant evidence at 0.05 level that the population moisture content is less than 0.35

as we are interested in less than 0.35 , hence please note that this becomes a 1 sided left tail test

The test statistic is calculated as: Tu

t critical value t value mu 1.689 1.695 from t tables -1.48078 -3.15158 0.35 0.35 given 31 0.316667 0.273548 0.135064 0.135064 36 Mean SD Boston Vermont 0.44 0.14 0.61 0.15 0.47 0.31 0.3 0.16 0.15 0.37 0.24 0.18 0.16 0.42 0.2 0.58 0.21 0.25 0.2 0.41 0.26 0.17 0.14 0.13 0.331 0.23 0.131 0.11

from t tables t critical value t value mu given 1.689 1.695 =(B6-B4)(B7/SQRT(B5)) =(C6-C4)(C7/SQRT(C5)) 0.35 0.35 =COUNT(B10:B45) =COUNT(C10:C45) =AVERAGE(B10:B45) -AVERAGE(C10:C40) =STDEV.P(C10:C40) ESTDEV.P(C10:C40) Mean SD Vermont 0.14 10.15 0.31 0.16 0.37 Boston 0.44 0.61 0.47 0.3 0.15 0.24 0.16 0.2 0.2 0.2 0.26 0.14 0.33 0.18 0.42 0.58 0.25 0.41 0.17 0.13 0.23 o

c) Even for Vermont shingles the procedure remains the same

just replace boston shinles data with vermont shingles

For boston shingles

as we see that the critical value is 1.689 which is not less than -1.48 , hence we fail to reject the null hypothesis and conclude that the result is not signficant and conclude that

There is no evidence at 0.05 level that the population moisture content is less than 0.35

For vermont shingles

as we see that the critical value is 1.695 which is not less than -3.15, hence we fail to reject the null hypothesis and conclude that the result is not signficant and conclude that

There is no evidence at 0.05 level that the population moisture content is less than 0.35