Posted by Richard on .
The Deborah Heart Institute performs many openheart 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.

Statistics 
MathGuru,
Try a onesample ztest.
Hypotheses:
Ho: µ = 42 >null hypothesis
Ha: µ < 42 >alternate hypothesis
z = (sample mean  population mean)/(standard deviation divided by the square root of the sample size)
With your data:
z = (40.2  42)/(5/√36) = ?
Finish the calculation.
Check a ztable at the level you wish to use for the rejection region.
If the ztest statistic exceeds that value from the ztable, reject the null and conclude µ < 42. If the ztest statistic does not exceed the that value from the ztable, do not reject the null (you cannot conclude a difference).
I hope this will help get you started.