.ll Verizon2:09 PM@ 31%Chapter 9 and 10...3. One indicator of physical fitness is resting pulse rate. Ten men were randomly selected to testan exercise device advertised on television by using it 3 times a week for 20 minutes. Theirresting pulse rates (beats per minute) were measured before the test began, and then againafter 6 weeks. Results are shown in the table below. Assuming differences are Normallydistributed, is there evidence that this kind of exercise can reduce resting pulse rates? Use a 1%level of significance.Pulse rate after (bpm)Pulse rate before (bpm)|75SubjectAllen73Brandon8179Carlos8281David8786Edwin9187Franco9991Graeme84Hans8583Ivan8384Jorge7976a.State the null and alternative hypothesesHo:H,:b. What calculator test will you use? List the requirements that must be met to use this test,and indicate whether the conditions are met in this problem.c. Run the calculator test and obtain the P-value.d. Based on your P-value, will you reject or fail to reject the null hypothesis?e. Interpret your conclusion from part d in the context of this problem.300000DashboardCalendarTo DoNotificationsInbox因

Data given is relating to pulse rate of 10 members before and after the exercise test. Let n= sample size = 10(a). Null hypothesis H0: There is no significant decrease in the pulse rate after the exercise test i.e., μ1 = μ2 Alternative hypothesis H1: There is no significant decrease in the pulse rate after the exercise test i.e., μ1 > μ2 Since the alternative hypothesis is greater than type, the test is a right tailed test. Level of significance α = 1% = 0.01(b). Here given that the difference of scores is normally distributed sample size n = 10 < 30 a small sample Sample observations are independent Population standard deviation is unknown Therefore all the requirements of t-test are satisfied. Hence use t-test for related samples. Critical value of Z t χ2 at α = 5% = 0.05 level of significance for two right left tailed test with ( ) degrees of freedomConclusion: Since the calculated value of Z = < critical value of Z = , accept reject null hypothesis H0.More clearly, (c). Before X After Y d = X - Y d2 75 73 2 4 81 79 2 4 82 81 1 1 87 86 1 1 91 87 4 16 99 91 8 64 87 84 3 9 85 83 2 4 83 84 -1 1 79 76 3 9 Total 25 113The test statistic t follows t-distribution with (n - 1) = 9 degrees of freedom. p-value = P(t > 3.3374) is obtained using MS-EXCEL function as follows = T.DIST.RT(X,DEG-FREEDOM) = T.DIST.RT(3.3374,9) = 0.0043(d). Since the p-value = 0.0043 < level of significance = 0.01, reject the null hypothesis. (e). Conclusion: There is an evidence that the kind of exercise can reduce resting pulse rates.