Answer Happy

Espanol For a certain knee surgery, a mean recovery time of 10 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, u, is less than 10 weeks. In a random sample of 46 knee surgery patients who practiced this new physical therapy, the mean recovery time is 9.7 weeks. Assume that the population standard deviation of recovery times is known to be 1.5 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 10 weeks? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis H. and the alternative hypothesis H. р X H: H: 0 H:1 O<0 oso oo OD D=D х 5 ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. x- -u • The value of the test statistic is given by 6 Jn • p- • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. : . One-tailed Two-tailed 03 Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.2+ Step 3: Shade the area represented by the p-value 0.1 Step 4: Enter the p-value. (Round to 3 decimal places.) 1 х X 5 $ ? (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 is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical х X 5 therapy is less than 10 weeks. ? Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not 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 10 weeks. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, 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 10 weeks. Since the p-value is greater than the level of significance, the null hypothesis is not 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 10 weeks.