Mountain States Surgery Center in Denver, Colorado, performs many knee replacement surgery procedures each year. Recently, research physicians at Mountain States have developed a surgery process they believe will reduce the average patient recovery time. The hospital board will not recommend the new procedure unless there is substantial evidence to suggest that it is better than the existing procedure. Records indicate that the current mean recovery rate for the standard procedure is 142 days, with a standard deviation of 15 days. To test whether the new procedure actually results in a lower mean recovery time, the procedure was performed on a random sample of 36 patients and found a sample mean of 140.2 days. Conduct a hypothesis test with the probability of making a Type I error is 5%.
State the null and alternate hypotheses
State the level of significance (alpha)
Compute the value of the test statistic
Determine the critical value and the decision rule
State your conclusion
Find the p value