Question

ONLY ANSWER Q1 Part 2

Question 1)

8.68 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 the entire 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 via a laboratory 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. In this situation, a shingle should experience no more than 0.8 grams of granule loss if it is expected to last the length of the warranty period. The file GranuleGranule table with 1 row and 1 column , row1 column 1 , cap granule , end table 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, construct a 95% confidence interval estimate for the mean granule loss. (Round to 2 decimal places)

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.142382504
Sample Mean	0.26
Sample Size	170
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.01092024
Degrees of Freedom	169
t Value	1.9741
Interval Half Width	0.0216
Confidence Interval
Interval Lower Limit	0.24
Interval Upper Limit	0.29

What kind of test is this?

Q1 Part 2) ---------------------------------------------------------------------------------------------------------------------------

Using the same data as the confidence interval, you wish to know if the mean loss of granule for the shingles is different than .25 grams. Below is the output for the necessary test.

At a 5% level of significance, is the mean loss of granule in shingles different than .25 grams? How does this confirm/deny your confidence interval in part 1?

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0.25
Level of Significance	0.05
Sample Size	170
Sample Mean	0.26
Sample Standard Deviation	0.1423825
Intermediate Calculations
Standard Error of the Mean	0.0109
Degrees of Freedom	169
t Test Statistic	0.9157
Two-Tail Test
Lower Critical Value	-1.9741
Upper Critical Value	1.9741
p-Value	0.3611
Do not reject the null hypothesis

Answer 1

Solution-1:

Ho:mu=0.25

Ha:mu nit =0.25

alpha=0.05

95% confidence for mean is 0.24 to 0.29

Hypothesized mean value of 0.25 lies within this confidence interval

0.24<0.25<0.29

Do not reject the null Hypothesis

Accept null hypothesis

Concluion:

there is no sufficient statistical evidence at 5% level of significance to conclude that he mean loss of granule in shingles different than .25 grams