For a certain knee surgery, a mean recovery time of 13 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time,H. is less than 13 weeks. In a random sample of 32 knee surgery patients who practiced this new physical therapy, the mean recovery time is 12.6 weeks.Assume that the population standard deviation of recovery times is known to be 1.2 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 13 weeks?Perform a hypothesis test, using the 0.10 level of significance.(a) State the null hypothesis H, and the alternative hypothesis H-H: 0OsDH:?(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 DistributionStup 1: Select ane-tailed or twa-tailed.O On-taledO Two-tailedStep 2: Enter the test statisti.(Round to 3 decimal places.)Step 3: Shade the area represnted 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 0.10 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 reoovery time of patients who practice the new style of physicaltherapy is less than 13 weeks.?O since the p-value is less than (or equal to) the level of significance, the null hypothesis is nat rejected. So, there isnot enough evidence to support the daim that the mean recovery time of patients who practice the new style afphysical therapy is less than 13 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 13 weeks.O since the p-value is greater than the level of significance, the null hypothesis is nat 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 13 weeks.Ix

Answered: Image /qna-images/answer/4be3e517-3a33-45c8-9026-5d0299b20f87.jpg

For a certain knee surgery, a mean recovery time of 13 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, H. is less than 13 weeks. In a random sample of 32 knee surgery patients who practiced this new physical therapy, the mean recovery time is 12.6 weeks. Assume that the population standard deviation of recovery times is known to be 12 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 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H- (b) Perform a 2-test and find the p-value. Here is some information to help you with your 2-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 Distribution Stup 1: Selea onetaled or two tailad. O Onetaled O Teo taled Stup 2: Enter the test stati. (Round to 3 decimal placs.) Stup a: Shade the area represente by the pvalu Stup 4 Entur the pvala. (Round to a deumal placs.) (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 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. Sa, there is encugh evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks. O since the p-value is less than (or equal to) the level of significance, the null hypothesis is nat rejected. So, there is not enough evidence to support the dlaim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks. O since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks. O since the p-value is greater than the level of significance, the null hypothesis is nat rejected. So, there is not enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks.