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 σ = 2.2 days. The hospital is trying a new recovery program designed to lessen the time patients spend in the hospital. The first 25 appendix patients in this new program were released from the hospital in an average of 5.5 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 .01 level of significance.Q61:The appropriate statistical procedure for this example would be aA.z-testB.t-testQ62:Is this a one-tailed or a two-tailed test?A.one-tailedB.two-tailed

9Q63:The most appropriate null hypothesis (in words) would beA.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.Q64:The most appropriate null hypothesis (in symbols) would beA.μnew program= 6.3B.μnew program= 5.5C.μnew program6.3D.μnew program6.3Q65:Set up the criteria for making a decision. That is, find the critical value using an alpha = .01. (Make sure you are sign specific: + ; -; or ) (Use your tables)Summarize the data into the appropriate test statistic.Steps:Q66:What is the numeric value of your standard error?Q67:What is the z-value or t-value you obtained (your test statistic)?Q68:Based on your results (and comparing your Q67 and Q65 answers) would youA.reject the null hypothesisB.fail to reject the null hypothesisQ69:The best conclusion for this example would beA.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.

10Q70:Based on your evaluation of the null in Q68 and your conclusion is Q69, as a researcher you would be more concerned with aA.Type I statistical errorB.Type II statistical errorCalculate the 99%confidence interval.Steps:Q71:The mean you will use for this calculation isA.5.5B.6.3Q72:What is the new critical value you will use for this calculation?Q73:As you know, two values will be required to complete the following equation:__________ ________

Answer 1

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 σ = 2.2 days. The hospital is trying a new recovery program designed to lessen the time patients spend in the hospital. The first 25 appendix patients in this new program were released from the hospital in an average of 5.5 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 .01 level of significance.

Q61:The appropriate statistical procedure for this example would be a

A.z-test

Q62 A.one-tailed

9Q63: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.

Q64:The most appropriate null hypothesis (in symbols) would be

A.μnew program= 6.3

using minitab>stat>basic stat>one sample z

we have

One-Sample Z

Test of μ = 6.3 vs < 6.3
The assumed standard deviation = 2.2

N Mean SE Mean 99% CI Z P
25 5.500 0.440 (4.367, 6.633) -1.82 0.035

Q65:we will reject Ho if z < -2.3263

Q66:the numeric value of your standard error is 0.440

Q67: the z-value = -1.82

Q68:B.fail to reject the null hypothesis

Q69:The best conclusion for this example 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.

Calculate the 99%confidence interval.Steps:Q71:The mean you will use for this calculation is 5.5

Q72:What is the new critical value 2.578

Q73:As you know, two values will be required to complete the following equation: 5.5 +/- 1.1334