1. My coach thinks that the average time to run a 5k fun run is 34 minutes. Suppose I simple randomly sample 46 people during a 5k fun run and find the sample average run time is 32.4 minutes and the sample standard deviation is 6.3 minutes. Test the hypothesis that the true (population) mean run time differs from 34 minutes. Use a significance level = alpha = 0.05. a. Which Type of test would you use: b. State your hypotheses c. Check your assumptions. d. State the Test Statistic: (2 decimal places each) and the p-value: (3 decimal places each) e. State a conclusion in the context of the problem: 1. Because my p-value is alpha, I the null. 2. Circle the correct conclusion: There is enough evidence to indicate that the true mean run time differs from 34 minutes. There is not enough evidence to indicate that the true mean run time differs from 34 minutes. 2. Continuing question I above. a. Calculate a 95% Confidence Interval for the true mean run time (make sure to show which calculator function you used.) b. Using your answer in a, would you decide to reject the null hypothesis or not reject BASED ON THIS CONFIDENCE INTERVAL? Why or why not