answer the question 2a-2e

2. A beer distributor sells kegs which are advertised to contain 15.5 gal of beer. A statistics student wants to ensure that the distributor is honest. The student selects a simple random sample of , = 10 kegs and finds a sample mean of x = 15.2 gal and a sample standard deviation of s = 0.6 gal. Assume the population distribution of keg quantities is approximately normal. Use an a = 0.10 significance level to test the claim that the kegs have a mean less than 15.5 gal. a. State the null and alternative hypotheses b. Find the critical value (CV) and indicate which is the claim c. Find the test statistic (TS) d. Sketch and label the following on the graph: u, x, TS. CV, and shade the critical region e. State the conclusion about Ho and the final conclusion regarding the original claim. f. What is a Type I error? What is the probability of making a Type I error for this hypothesis test? g. What is the critical value if we use a significance level a = 0.05? Does the conclusion about Ho change? If yes, what is the new statement about the final conclusion regarding the original claim? h. Assume the population standard deviation was known to be a = 0.6 gallons. Find the test statistic for o known. Use the test statistic to find the P-value. Use the P-value method to determine the conclusion about Ho (use a = 0.01). Explain your answer. i. Explain what the P-value means