Exercise 14.4: The mid-distance running coach, Zdravko Popovich, for the Olympic team of an eastern European country claims that his six-month training program significantly reduces the average time to complete a 1500-meter run. Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training program, and their completion times (in minutes) of the 1500- meter run were recorded. After six months of training under coach Popovich, the same five runners' 1500- meter run times were recorded again. The results are given below. We want to test Runner Completion Time Before After Di = Time before - Time after (Di - d ) Training Training 5.9 5.4 5.9-5.4 = 0.5 (0.5-0.28)2 = 0.0484 7.5 7.1 7.5-7.1 = 0.4 (0.4-0.28)2 = 0.0144 6.1 6.2 6.8 6.5 8.1 7.8 E(Di - d ) 2 =? a. Compute Di for runners 3, 4, and 5. b. Let d = average of Di = 0.28 c. Compute standard deviation Sd. Note sa = [(Di-d) 2 n-1 , and $d= Isa d. Construction a hypothesis test hypothesis to determine, at significant level of 0.05, whether there has been a significant decrease in mean time per mile. Let Us = WTineRetainedter (1) Use critical value approach in the test. What is your conclusion? (2) If the p-value is 0.0445 for the test, what is your conclusion? Exercise 14.5: Suppose that we wish to test Ho: HI -12=0 versus HA: HI - H2 # 0, where nj = 7 and n2 = 7 from two normally distributed populations having u and u2, and suppose we obtain x, = 225, x, = 210, s, =4 and s, = 5. Under the assumption of the unequal variances, test the null hypothesis. Use df = 11 and a =0.05.Problem I. For each of the following null hypotheses and given o levels and assuming equal population variances State the alternative hypothesis. Label the value of the critical value in t on the bottom axis. (iii) Draw and shade the appropriate rejection region. (iv) State the decision rule. a. H. : H, - M, =0 where ni = 19 and n2 = 16 ;_Ha : 4 = 0.02 Decision Rule: b. H. : H - H, SO where n, = 18 and n2 = 20; Ha :