8. A researcher thinks that if hip-surgery patients go to physical therapy three times a week, instead of the usual twice a week, their recovery period will be shorter. In

the past, population mean recovery time for hip-surgery patients who attended twice a week was 8.2 weeks. A random sample of 81 hip-surgery patients is selected. Each patient is asked to attend physical therapy three times a week. The sample results show a mean recovery time of 7.7 weeks and a standard deviation of 3.15 weeks.Using a 5% level of significance, can the researcher conclude that the mean recovery time has decreased with more physical therapy? Formulate and test the appropriate hypotheses, using both the critical value approach and the P-value approach. Provide a concluding statement, interpreted within the context of the question.Note: When you consult the appropriate statistical table to answer this question, use the degrees of freedom in the row following "T =75 (where infinity shows as the T ). Critical value approach p-valueаpproach