The Deborah Heart Institute performs many open-heart surgery procedures. Recently research physicians at the Institute developed a new heart bypass procedure that they believe reduces the average length of recovery. The hospital board will not adopt the procedure unless there is substantial evidence to suggest that it is better than the current procedure. Records indicate that the mean recovery rate for the current procedure is 42 days with a standard deviation of 5 days. Test this hypothesis on a sample=36 patients and a sample mean of 40.2 days using a rejection region.

Question

The Deborah Heart Institute performs many open-heart surgery procedures. Recently research physicians at the Institute developed a new heart bypass procedure that they believe reduces the average length of recovery. The hospital board will not adopt the procedure unless there is substantial evidence to suggest that it is better than the current procedure. Records indicate that the mean recovery rate for the current procedure is 42 days with a standard deviation of 5 days. Test this hypothesis on a sample=36 patients and a sample mean of 40.2 days using a rejection region. 
(can you provide complete answer with detailed steps)

PsyDAG · Answer

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.