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A pharmaceutical company claims that they have a new drug that will significantly reduce the average recovery time for a particular operation. Until now the mean recovery time has been 21.7 hours. The next 22 patients having this operation at a large teaching hospital are treated with the new drug and the average recovery time for these patients is found to be 20.3 hours with a standard deviation of 3.47 hours. Do the data support the pharmaceutical company's claim? Test the appropriate hypothesis at a = 0.10. (a). The null and alternative hypotheses are Ο H0: μ= 21.7 Ha:µ > 21.7 O Ho: µ = 20.3 Ha:µ < 20.3 O Ho: µ = 21.7 Ha:µ < 21.7 O Ho:ã = 20.3 Ha:ã < 20.3 Part 2 of 6 (b). The test statistic is (use 4 decimal places)

A pharmaceutical company claims that they have a new drug that will significantly reduce the average recovery time for a particular operation. Until now the mean recovery time has been 21.7 hours. The next 22 patients having this operation at a large teaching hospital are treated with the new drug and the average recovery time for these patients is found to be 20.3 hours with a standard deviation of 3.47 hours. Do the data support the pharmaceutical company's claim? Test the appropriate hypothesis at a = 0.10. (a). The null and alternative hypotheses are Ο H0: μ= 21.7 Ha:µ > 21.7 O Ho: µ = 20.3 Ha:µ < 20.3 O Ho: µ = 21.7 Ha:µ < 21.7 O Ho:ã = 20.3 Ha:ã < 20.3 Part 2 of 6 (b). The test statistic is (use 4 decimal places)

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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**Hypothesis Testing: Reducing Recovery Time with a New Drug** A pharmaceutical company claims that a new drug will significantly reduce the average recovery time for a specific operation. Historically, the mean recovery time has been 21.7 hours. During a trial, 22 patients at a large teaching hospital were treated with this new drug, and their average recovery time was 20.3 hours with a standard deviation of 3.47 hours. We are tasked with determining if the data supports the company's claim using a hypothesis test at a significance level (\(\alpha\)) of 0.10. (a) **Null and Alternative Hypotheses:** - **Null Hypothesis (\(H_0\))**: \(\mu = 21.7\) - **Alternative Hypothesis (\(H_a\))**: \(\mu < 21.7\) Here, the selected hypothesis tests whether the mean recovery time with the new drug (\(\mu\)) is less than 21.7 hours. (b) **Test Statistic:** To determine if the results are statistically significant, calculate the test statistic, ensuring it is rounded to four decimal places. The box for entering this value is provided in the text.
Transcribed Image Text:**Hypothesis Testing: Reducing Recovery Time with a New Drug** A pharmaceutical company claims that a new drug will significantly reduce the average recovery time for a specific operation. Historically, the mean recovery time has been 21.7 hours. During a trial, 22 patients at a large teaching hospital were treated with this new drug, and their average recovery time was 20.3 hours with a standard deviation of 3.47 hours. We are tasked with determining if the data supports the company's claim using a hypothesis test at a significance level (\(\alpha\)) of 0.10. (a) **Null and Alternative Hypotheses:** - **Null Hypothesis (\(H_0\))**: \(\mu = 21.7\) - **Alternative Hypothesis (\(H_a\))**: \(\mu < 21.7\) Here, the selected hypothesis tests whether the mean recovery time with the new drug (\(\mu\)) is less than 21.7 hours. (b) **Test Statistic:** To determine if the results are statistically significant, calculate the test statistic, ensuring it is rounded to four decimal places. The box for entering this value is provided in the text.
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