Question

The following 13 questions (Q1 to Q13) are based on the following example:

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 = 1.2 days. The hospital is trying a new recovery program designed to lessen the time patients spend in the hospital. The first 10 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 .05 level of significance.

The appropriate statistical procedure for this example would be a?

A. z - test
B. t - test

Answer 1

For a small sample size of 10 and a known population standard deviation, a t-test is used to determine if there is a significant reduction in recovery time.

Step-by-step explanation:

The appropriate statistical procedure to determine if the new program has led to a significant reduction in recovery time, given that the sample size is 10, which is less than 30, and the population standard deviation is known is a t-test.

Since the sample size is small and we are comparing the sample mean to the population mean, the t-test is the appropriate choice for this situation. A z-test would be appropriate if the sample size were large (n > 30) or if the population variance were known and the sample size were smaller than 30 but the distribution were normal.