Question 12 12 pts A machine is designed to produce washers with a mean thickness of 0.220 cm. It may be assumed that the thickness of washers produced by the machine follows a normal distribution. A random sample of 10 washers from the machine has a sample mean of 0.231 cm and a sample variance of 0.000144 cm2. Let / denote the mean thickness of the washers produced by the machine. (a) Carry out a two-tailed test of the null hypothesis Ho : / = 0.220 versus the alternative H1 : / # 0.220 with the level of significance o = 5%. Consider the following regions: Region A: (-00, 0.213) U (0.227, co) Region B: (-0o, 0.224) U (0.238, co) Region C: (-0o, 0.211) U (0.229, co) Which of the above regions, if any, is the critical (rejection) region for the test. Enter A, B or C in the answer box for regions A, B or C respectively. If none of them is the correct critical region, enter N in the answer box. Answer: (b) What is the conclusion of the test? In the answer box, enter R for 'reject Ho' and DNR for 'do not reject Ho' If the test is inconclusive, enter N. Answer: (c) What is the p-value of the test? Give your answer to 3 decimal places in the answer box. Answer: Question 13 6 pts A farm claims that the chicken eggs it produces contains 6.80g of protein on average. A large sample of eggs taken at random from the farm yields a sample mean of 6.10g of protein. Using the sample, a 95% confidence level for the population mean is constructed as (5.36, 6.84). Let / denote the average amount of protein (in g) in the eggs produced at the farm. (a) A two-tail test of the null hypothesis Ho : A = 6.80 versus the alternative #1 : / # 6.80 at the 5%% level of significance is carried out. What is the conclusion of the test? In the answer box, enter R for 'reject Ho' and enter DNR for 'do not reject Ho' Enter N if there is insufficient information to draw a conclusion. Answer: (b) A one-tail test of the null hypothesis Ho : A = 6.80 versus the alternative hypothesis #1 : A