Patients recovering from an appendix operation normally spend an average of 6.3
ID: 3245601 • Letter: P
Question
Patients recovering from an appendix operation normally spend an average of 6.3 days in the hospital. The distribution of recovery times is normal with a sigma = 2.0 days. The hospital is trying a new recovery program designed to lessen the time patients spend in the hospital. The first 16 appendix patients in this new program were released from the hospital in an average of 5.8 days. On the basis of these data, can the hospital conclude that the new program has a significant reduction of recovery time. Test at the 05 level of significance. The appropriate statistical procedure for this example would be a A. t-test B. z-test Is this a one-tailed or a two-tailed test? A. one-tailed B. two-tailed The most appropriate null hypothesis (in words) would be A. There is no statistical difference in the amount of time appendix patients spend in the hospital when comparing the new recovery program to the population of patients on the traditional recovery program. B. There is a statistical difference in the amount of time appendix patients spend in the hospital when comparing the new recovery program to the population of patients on the traditional recovery program. C. The new appendix recovery program does not significantly reduce the number of days spent in the hospital when compared to the population of patients on the traditional recovery program. D. The new appendix recovery program does significantly reduce the number of days spent in the hospital when compared to the population of patients on the traditional recovery program. The most appropriate null hypothesis (in symbols) would be A.middotmu_new program = 6.3 B.middotmu_new program = 5.8 C. mu_new program lessthanorequalto 6.3 D. mu_new program greaterthanorequalto 6.3 Set up the criteria for making a decision. That is, find the critical value using an alpha = 05.(Make sure you are sign specific: +: -: or plusminus) (Use your tables) Summarize the data into the appropriate test statistic. Steps: What is the numeric value of your standard error?Explanation / Answer
1) z-test is used as population variance is known
2) this is one-tailed test as we want to check if mean has reduced or not
3) option A ) is correct
4)option C) is correct as we want to check if mean has reduced or not
5) critical value for alpha = 0.05 is -1.645
TS = (Xbar -mu)/(s/sqrt(n) = (5.8-6.3)/(2/sqrt(16)) =-1
6) since -1 > -1.645 ,
we fail to reject the null hypothesis
standard error = (2/sqrt(16)) = 2/4 = 0.5