Question 3: (40 pts. ) The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 25 throws. For the 25 throws, Marco's mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a = 5%. Assume the throw distances for footballs are normal. First, determine what type of test this is, set up the hypothesis test, find the p-value, sketch the graph, compare the p-value and o, and state your decision & conclusion. Show all five steps for full credits: a = 58 = 0.05 H = 40 & 0 = 2 From the given data, we have: Sample size = 25 & sample mean = 45 Step 1: Set up the Hypothesis Test: Since the problem is about the mean distance, this is a test of a single population mean. Ho : H Ha: |1 Step 2: Determine the distribution needed: Marco Random variable: * = the mean distance, in yards, threw by Distribution for the test: Step 3: Calculate the p-value: Step 4: Compare a and the p-value: Make a Decision: Step 5: Write a Conclusion: At the 58 level of significance