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For a certain knee surgery a mean recovery time of 11 weeks is typical With a new style of physical therapy a researcher claims that the mean recovery time is less than 11 weeks In a random sample of 37 knee surgery patients who practiced this new physical therapy the mean recovery time is 10 6 weeks Assume that the population standard deviation of recovery times is known to be 2 1 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 11 weeks Perform a hypothesis test using the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H Ho H 0 given by 7 b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test 0 n Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two talled 0 05 is the value that cuts off an area of 0 05 in the right tail The test statistic has a normal distribution and the value is Step 2 Enter the critical value s Round to 3 decimal places Step 3 Enter the test statistic Round to 3 decimal places 0 3 02 0 1 Since the value of the test statistic lies in the rejection region 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 11 weeks H Since the value of the test statistic lies in the rejection region 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 11 weeks O O Since the value of the test statistic doesn t lie in the rejection region 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 11 weeks Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean recovery time of patients who X 020 0 0 0 0 X 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 OSO O X S E E

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