Please answer the two questios well

2. [Quit Smoking Or Not] [20 points] A study was done to identify factors affecting physicians' decisions to advise or not to advise pa- tients to stop smoking (Cummings et al. 1987). The study was related to a training program to teach physicians ways to counsel patients to stop smoking and was carried out in a family practice outpatient center in Buffalo, New York. The study population consisted of the cigarette-smoking patients of residents in family medicine seen in the center between February and May 1984. We first consider whether certain patient characteristics are related to being advised or not being advised. The following table shows a breakdown by gender of the patient: Advised Not Advised Male 18 47 Female 80 136 (a) [4 points) What proportion of the males were advised to quit and what proportion of the females were advised? What are the standard errors of these proportions? (As the sample size is fairly large, do not use the Wilson plus four estimate.)3. [Heat Enduring Glass] [18 points] A firm producing plate glass has developed a new process meant to allow glass for fireplaces to rise to a higher temperature before breaking. To test the process, plates of glass are drawn randomly from a production run. Data are collected on the breaking temperature using the old process and the new process. The data appear below: Breaking Temperature New Old Difference 487 475 12 440 436 495 495 0 488 483 5 435 426 9 sample mean 469 463 6 sample SD 28.97 30.27 4.64 For this problem, let Anew be the population mean breaking temperature using the new process and Hold be the population mean breaking temperature using the old process. (a) [8 points] Suppose the experiment is done using a completely randomized design. That is, a sample of 10 glasses are selected, and randomly assign 5 of them to undergo the new process, and the remaining 5 to undergo the old process. Test Ho: Anew = Hold versus Ha: Anew > Hold- Give the test-statistic and P-value and make con- clusion using significance level o = 0.01. Assume the population SDs are EQUAL (01 = 02)