For a certain knee surgery, a mean recovery time of 9 weeks is typical. With a new style of physical therapy, a researcher dlaims that the mean recovery time,ETu, is less than 9 weeks. In a random sample of 84 knee surgery patients who practiced this new physical therapy, the mean recovery time is 8.9 weeks. Assumethat the population standard deviation of recovery times is known to be 0.9 weeks.Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 9 weeks?Perform a hypothesis test, using the 0.05 level of significance.(a) State the null hypothesis H, and the alternative hypothesis H.Hg: 0OsOO20O=0?(b) Perform a Z-test and find the p-value.Here is some information to help you with your Z-test.• The value of the test statistic is given by• The p-value is the area under the curve to the left of the value of the test statistic.Standard Normal Distribution0.4Step 1: Select one-tailed or two-tailed.O One-tailedO Two-tailedStep 2: Enter the test statistic.(Round to 3 decimal places.)02-Step 3: Shade the area represented bythe p-value.Step 4: Enter the p-value.(Round to 3 decimal places.) (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the researcher.O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there isenough evidence to support the claim that the mean recovery time of patients who practice the new style of physicaltherapy is less than 9 weeks.O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there isnot enough evidence to support the claim that the mean recovery time of patients who practice the new style ofphysical therapy is less than 9 weeks.O Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enoughevidence to support the claim that the mean recovery time of patients who practice the new style of physical therapyis less than 9 weeks.O ince the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enoughevidence to support the claim that the mean recovery time of patients who practice the new style of physical therapyis less than 9 weeks.

Question

Accepted Answer

For the given data
Perform Z test for one mean