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 ? = 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.

Summarize the data into the appropriate test statistic. Steps:

Q6: What is the numeric value of your standard error?

Q7: What is the z-value or t-value you obtained (your test statistic)?

Q8: Based on your results would you

A. reject the null hypothesis

B. fail to reject the null hypothesis

Q9: 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.

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.

Q10: Based on your evaluation of the null in Q8 and your conclusion is Q9, as a researcher you would be more concerned with a

A. Type I statistical error

B. Type II statistical error

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
? : Mean of population
H₀ : ? = 6.3
H_A : ? < 6.3
Standard deviation = 2.2

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
?	25	5.5	0.44	-1.8181818	0.0345

Hence,

Standard error = 0.44

z - value = -1.8182

Fail to reject the null hypothesis

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. Option C is correct.

Type II statistical error