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1-> A research report claims that mice with an average life span of 32 months will live to be about 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. placed on this diet have an average life of 40 months with a standard deviation of 3.3 months? Use a P-value in your conclusion. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. O O O O O O O Identify the null and alternative hypotheses. OA. Ho: H=41 H₁ #41 D. Ho: H=41 H₁ <41 Find the test statistic. -2.46 (Round to two decimal places as needed.) Determine the range into which the P-value falls. 0.0075 ≤ P-value < 0.01 What is the appropriate conclusion for this test? Ho and conclude that there Ο Β. Ηο:μπ 41 H₁ > 41 OE. Ho: > 41 H₁ 41 sufficient evidence that mice with an average life span of 32 months will live to be OC. Ho: <41 H₁: p=41 OF. Ho: #41 H₁: =41 there any reason to believe that u <41 if 66 mice that are than 41 months old when 40% of the calories in their diet are replaced by vitamins and protein.

1-> A research report claims that mice with an average life span of 32 months will live to be about 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. placed on this diet have an average life of 40 months with a standard deviation of 3.3 months? Use a P-value in your conclusion. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. O O O O O O O Identify the null and alternative hypotheses. OA. Ho: H=41 H₁ #41 D. Ho: H=41 H₁ <41 Find the test statistic. -2.46 (Round to two decimal places as needed.) Determine the range into which the P-value falls. 0.0075 ≤ P-value < 0.01 What is the appropriate conclusion for this test? Ho and conclude that there Ο Β. Ηο:μπ 41 H₁ > 41 OE. Ho: > 41 H₁ 41 sufficient evidence that mice with an average life span of 32 months will live to be OC. Ho: <41 H₁: p=41 OF. Ho: #41 H₁: =41 there any reason to believe that u <41 if 66 mice that are than 41 months old when 40% of the calories in their diet are replaced by vitamins and protein.

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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### Statistical Hypothesis Testing with Mice Lifespan A research report claims that mice with an average lifespan of 32 months will live to be about 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. We are tasked with determining if there is any reason to believe that the mean lifespan \( \mu < 41 \) for 66 mice on this diet, given an average lifespan of 40 months with a standard deviation of 3.3 months. A P-value will be used in drawing conclusions. #### Steps for Hypothesis Testing 1. **Identify the Null and Alternative Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 41 \) - Alternative Hypothesis (\( H_1 \)): \( \mu < 41 \) - Correct Selection: Option D 2. **Find the Test Statistic:** - The test statistic calculated is \(-2.46\) (rounded to two decimal places as needed). 3. **Determine the P-value Range:** - The P-value falls within the range: \( 0.0075 < \text{P-value} < 0.01 \). 4. **Conclusion Based on P-value:** - Decision: Reject \( H_0 \) - Conclusion: There is sufficient evidence that mice with an average lifespan of 32 months will live to be **less** than 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. ### Additional Resources - Click to view statistical tables for critical values of the t-distribution: - [Page 1 of the table of critical values](#) - [Page 2 of the table of critical values](#) This analysis demonstrates the application of hypothesis testing in determining the effect of dietary changes on the lifespans of mice using statistical tools and critical value tables.
Transcribed Image Text:### Statistical Hypothesis Testing with Mice Lifespan A research report claims that mice with an average lifespan of 32 months will live to be about 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. We are tasked with determining if there is any reason to believe that the mean lifespan \( \mu < 41 \) for 66 mice on this diet, given an average lifespan of 40 months with a standard deviation of 3.3 months. A P-value will be used in drawing conclusions. #### Steps for Hypothesis Testing 1. **Identify the Null and Alternative Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 41 \) - Alternative Hypothesis (\( H_1 \)): \( \mu < 41 \) - Correct Selection: Option D 2. **Find the Test Statistic:** - The test statistic calculated is \(-2.46\) (rounded to two decimal places as needed). 3. **Determine the P-value Range:** - The P-value falls within the range: \( 0.0075 < \text{P-value} < 0.01 \). 4. **Conclusion Based on P-value:** - Decision: Reject \( H_0 \) - Conclusion: There is sufficient evidence that mice with an average lifespan of 32 months will live to be **less** than 41 months old when 40% of the calories in their diet are replaced by vitamins and protein. ### Additional Resources - Click to view statistical tables for critical values of the t-distribution: - [Page 1 of the table of critical values](#) - [Page 2 of the table of critical values](#) This analysis demonstrates the application of hypothesis testing in determining the effect of dietary changes on the lifespans of mice using statistical tools and critical value tables.
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