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 thanweeks. 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 byStandard Normal DistributionStep 1: Select one-tailed or two-tailed.O One-tailedO Two-tailedx-μ0Step 2: Enter the test statistic.(Round to 3 decimal places.)HO (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-tailedo Two-tailedStep 2: Enter the teststatistic.(Round to 3 decimalplaces.)Step 3: Shade the arearepresented by the p-value.x-H.Step 4: Enter the p-value.(Round to 3 decimal.places.)0.30.20.1(c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claimmade by the researcher.Since the p-value is less than (or equal to) the level of significance, the null hypothesis isrejected. So, there is enough evidence to support the claim that the mean recovery time ofpatients 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 isnot rejected. So, there is not enough evidence to support the claim that the mean recoverytime 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 patientswho 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 notrejected. So, there is not enough evidence to support the claim that the mean recoverytime of patients who practice the new style of physical therapy is less than 9 weeks.

Solution: Given information: n=73 Sample sizex= 8.8 Sample mean μ=9 Population mean σ=0.9 Population…

Answered: For a certain knee surgery, a mean…

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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A particular IQ test is standardized to a Normal model, with a mean of 80 and a standard deviation of 8. A group of 8,000 people had participated in a study based on IQ. Using the Empirical rule determine about how many of them should have IQ scores more than 72?
A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 1.2 micrograms/mL, the researcher’s hypothesis, for a level of significance of 1%, should resemble which of the following sets of hypothesis? H0: µ = 3.7 micrograms/mL; H1: µ > 3.7 micrograms/mL; alpha= .01 H0: µ > 3.7 micrograms/mL; H1: µ = 3.7 micrograms/mL; alpha= .01 H0: µ = 3.7 micrograms/mL; H1: µ > 3.7 micrograms/mL; alpha= .99 H0: µ > 3.7 micrograms/mL; H1: µ = 3.7 micrograms/mL; alpha= .99
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A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like? Reject H0 if z is less than or equal to –2.326. Reject H0 if z is greater than or equal to 2.326. Reject H0 if z is less than or equal to –2.576. Reject H0 if z is greater than or equal to 2.5760

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