Front housings for cell phones are manufactured in an injection molding process. the time the part is allowed to cool in the mold before removal is thought to influence the occurrence of a particularly troublesome cosmetic defect, flow lines, in the finished housing. after manufacturing, the housings are inspected visually and assigned a score between 1 and 10 based on their appearance, with 10 corresponding to a perfect part and 1 corresponding to a completely defective part. an experiment was conducted using two cool-down times, 10 seconds and 20 seconds, and 20 housings were evaluated at each level of cool-down time. all 20 observations in this experiment were run in random order. the data is: 10 seconds 20 seconds
1 7
2 8
1 5
3 9
5 5
1 8
5 6
2 4
3 6
5 7
3 6
6 9
5 5
3 7
2 4
1 6
6 8
8 5
2 8
3 7 is there evidence to support the claim that longer cool down results in fewer appearance defects? write the hypotheses using mathematical notation, derive the test statistic and write the distribution of the test statistic under the null hypothesis, compute the p-value and draw your conclusions. use a=0.05.

find a 95% confidence interval for the difference between the means (between the 10-second cool down sample, and the 20-second sample).
check the assumptions. include appropriate plots, and comment on your findings.
what is your recommendation to the company?