Please show the formula used and for testing hypotheses question be sure to show all steps: null and alternative hypotheses, test statistics, rejection region, computation of test statistic, and conclusion. Thanks!

2. Manufacturer B also produces crankshafts for an automobile engine. The wear of the crankshaft after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of 25 shafts is tested and the sample mean and the sample standard are 2.78 and 1.0. It is known that the wear amount is normally distributed with an unknown mean (,u). (a) Test H9 : ,u : 3 versus using H1 : ,LL % 3 at signicance level a : 0.05. Use rejection region to do the test. (b) What is the p-Value of the test in (a)? Would you reject the null hypothesis at o; : 005?, at 04 = 001?? Why? 3. The sugar content of the syrup in canned peaches is normally distributed. A consumer wants to estimate the standard deviation of sugar content in these cans. A random sample of 10 cans yields a standard deviation of 4.8 milligrams. (a) Give a point estimate for the population standard deviation, 0. (b) Find a 95% condence interval for the population standard deviation. Give a practical interpretation for the