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For a certain knee surgery, a mean recovery time of 9 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, μ, is less than 9 weeks. In a random sample of 73 knee surgery patients who practiced this new physical therapy, the mean recovery time is 8.8 weeks. Assume that 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 Ho and the alternative hypothesis H₁. Ho: H₁:0 (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. H 0<0 X X OSO 020 0=0 O

For a certain knee surgery, a mean recovery time of 9 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, μ, is less than 9 weeks. In a random sample of 73 knee surgery patients who practiced this new physical therapy, the mean recovery time is 8.8 weeks. Assume that 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 Ho and the alternative hypothesis H₁. Ho: H₁:0 (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. H 0<0 X X OSO 020 0=0 O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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For a certain knee surgery, a mean recovery time of 9 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, μ, is less than weeks. In a random sample of 73 knee surgery patients who practiced this new physical therapy, the mean recovery time is 8.8 weeks. Assume that 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 Ho and the alternative hypothesis H₁. Ho: H₁: O (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 Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed x-μ 0 Step 2: Enter the test statistic. (Round to 3 decimal places.) H O<O OSO 8 020 X |x • The p-value is the area under the curve to the left of the value of the test statistic. 0=0 0#0 04 O<O 03+ S
Transcribed Image Text:For a certain knee surgery, a mean recovery time of 9 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, μ, is less than weeks. In a random sample of 73 knee surgery patients who practiced this new physical therapy, the mean recovery time is 8.8 weeks. Assume that 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 Ho and the alternative hypothesis H₁. Ho: H₁: O (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 Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed x-μ 0 Step 2: Enter the test statistic. (Round to 3 decimal places.) H O<O OSO 8 020 X |x • The p-value is the area under the curve to the left of the value of the test statistic. 0=0 0#0 04 O<O 03+ S
(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. O One-tailed o Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value. x-H. Step 4: Enter the p- value. (Round to 3 decimal. places.) 0.3 0.2 0.1 (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. 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 9 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 9 weeks. 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 9 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 9 weeks.
Transcribed Image Text:(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. O One-tailed o Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value. x-H. Step 4: Enter the p- value. (Round to 3 decimal. places.) 0.3 0.2 0.1 (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. 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 9 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 9 weeks. 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 9 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 9 weeks.
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