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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, μ, 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 12.8 weeks. Assume that the population standard deviation of recovery times is known to be 1.1 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 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. H Ho: O H₁:0 OO 020 ローロ OO ? (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 x-μ √n • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 04 Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 02+ Step 3: Shade the area represented by the p-value. 01+ Step 4: Enter the p-value. (Round to 3 decimal places.) X

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, μ, 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 12.8 weeks. Assume that the population standard deviation of recovery times is known to be 1.1 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 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. H Ho: O H₁:0 OO 020 ローロ OO ? (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 x-μ √n • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 04 Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 02+ Step 3: Shade the area represented by the p-value. 01+ Step 4: Enter the p-value. (Round to 3 decimal places.) X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(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 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. x O 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 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 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 13 weeks.
Transcribed Image Text:(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 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. x O 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 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 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 13 weeks.
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, μ, 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 12.8 weeks. Assume that the population standard deviation of recovery times is known to be 1.1 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 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. H Ho: O H₁:0 O<O OSO O>O 020 ローロ OO ? (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 x-μ √n • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 04 Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 02+ Step 3: Shade the area represented by the p-value. 01+ Step 4: Enter the p-value. (Round to 3 decimal places.) X
Transcribed Image Text: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, μ, 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 12.8 weeks. Assume that the population standard deviation of recovery times is known to be 1.1 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 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. H Ho: O H₁:0 O<O OSO O>O 020 ローロ OO ? (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 x-μ √n • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 04 Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 02+ Step 3: Shade the area represented by the p-value. 01+ Step 4: Enter the p-value. (Round to 3 decimal places.) X
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