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A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 299 vinyl gloves, 63% leaked viruses. Among 299 latex gloves, 14% leaked viruses. Using the accompanying display of the technology results, and using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Click the icon to view the technology results. What are the null and alternative hypotheses? OA. Ho: P₁ P2 H₁: P₁ = P2 O D. Ho: P1 P2 H₁: P₁ = P2 OB. Ho: P1 P2 H₁: P₁ P2 OE. Ho: P1 = P2 H₁: P₁ P2 ... OC. Ho: P1 P2 H₁: P₁ #P2 OF. Ho: P1 H₁: P₁ P2 P2

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 299 vinyl gloves, 63% leaked viruses. Among 299 latex gloves, 14% leaked viruses. Using the accompanying display of the technology results, and using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Click the icon to view the technology results. What are the null and alternative hypotheses? OA. Ho: P₁ P2 H₁: P₁ = P2 O D. Ho: P1 P2 H₁: P₁ = P2 OB. Ho: P1 P2 H₁: P₁ P2 OE. Ho: P1 = P2 H₁: P₁ P2 ... OC. Ho: P1 P2 H₁: P₁ #P2 OF. Ho: P1 H₁: P₁ P2 P2

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 for Laboratory Glove Leakage A newspaper reported a study where researchers assessed the stress resistance of different types of laboratory gloves. In this study, 299 vinyl gloves and 299 latex gloves were tested for virus leakage. The results were as follows: - Among vinyl gloves, 63% leaked viruses. - Among latex gloves, 14% leaked viruses. ### Objective Using the provided data, test the claim that vinyl gloves have a higher virus leak rate compared to latex gloves at a significance level of 0.01. Vinyl gloves are considered as population 1, and latex gloves as population 2. ### Hypotheses The research question can be formulated into the following null and alternative hypotheses: - **Null Hypothesis (\(H_0\))**: \(p_1 = p_2\) (The leak rates of vinyl and latex gloves are equal.) - **Alternative Hypothesis (\(H_1\))**: \(p_1 > p_2\) (The leak rate of vinyl gloves is higher than that of latex gloves.) ### Multiple-Choice Options From the given choices, identify the appropriate hypotheses: **Options:** - A. \(H_0: p_1 \ne p_2\); \(H_1: p_1 = p_2\) - B. \(H_0: p_1 = p_2\); \(H_1: p_1 < p_2\) - C. \(H_0: p_1 = p_2\); \(H_1: p_1 \ne p_2\) - D. \(H_0: p_1 < p_2\); \(H_1: p_1 = p_2\) - E. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\) - F. \(H_0: p_1 > p_2\); \(H_1: p_1 = p_2\) The correct choice aligning with our research question is: - **E. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\)** Understanding the hypotheses is crucial for proper statistical testing and validating the research claim.
Transcribed Image Text:### Hypothesis Testing for Laboratory Glove Leakage A newspaper reported a study where researchers assessed the stress resistance of different types of laboratory gloves. In this study, 299 vinyl gloves and 299 latex gloves were tested for virus leakage. The results were as follows: - Among vinyl gloves, 63% leaked viruses. - Among latex gloves, 14% leaked viruses. ### Objective Using the provided data, test the claim that vinyl gloves have a higher virus leak rate compared to latex gloves at a significance level of 0.01. Vinyl gloves are considered as population 1, and latex gloves as population 2. ### Hypotheses The research question can be formulated into the following null and alternative hypotheses: - **Null Hypothesis (\(H_0\))**: \(p_1 = p_2\) (The leak rates of vinyl and latex gloves are equal.) - **Alternative Hypothesis (\(H_1\))**: \(p_1 > p_2\) (The leak rate of vinyl gloves is higher than that of latex gloves.) ### Multiple-Choice Options From the given choices, identify the appropriate hypotheses: **Options:** - A. \(H_0: p_1 \ne p_2\); \(H_1: p_1 = p_2\) - B. \(H_0: p_1 = p_2\); \(H_1: p_1 < p_2\) - C. \(H_0: p_1 = p_2\); \(H_1: p_1 \ne p_2\) - D. \(H_0: p_1 < p_2\); \(H_1: p_1 = p_2\) - E. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\) - F. \(H_0: p_1 > p_2\); \(H_1: p_1 = p_2\) The correct choice aligning with our research question is: - **E. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\)** Understanding the hypotheses is crucial for proper statistical testing and validating the research claim.
### Technology Results #### Summary of Statistical Results - **Pooled Proportion:** 0.39 - **Test Statistic, \( z \):** 12.2523 - **Critical \( z \):** 2.3264 - **P-value:** 0.0000 #### 98% Confidence Interval \[ 0.4080586 < P_1 - P_2 < 0.5685300 \] #### Description This box summarizes the results of a statistical hypothesis test. The pooled proportion, test statistic (\( z \)), critical value of \( z \), and the p-value are presented. The result also includes the 98% confidence interval for the difference in proportions (\( P_1 - P_2 \)). The confidence interval indicates that we can be 98% confident that the true difference between the proportions falls within the given range. #### Additional Options The results can be printed or saved using the "Print" and "Done" buttons located at the bottom of the dialog window.
Transcribed Image Text:### Technology Results #### Summary of Statistical Results - **Pooled Proportion:** 0.39 - **Test Statistic, \( z \):** 12.2523 - **Critical \( z \):** 2.3264 - **P-value:** 0.0000 #### 98% Confidence Interval \[ 0.4080586 < P_1 - P_2 < 0.5685300 \] #### Description This box summarizes the results of a statistical hypothesis test. The pooled proportion, test statistic (\( z \)), critical value of \( z \), and the p-value are presented. The result also includes the 98% confidence interval for the difference in proportions (\( P_1 - P_2 \)). The confidence interval indicates that we can be 98% confident that the true difference between the proportions falls within the given range. #### Additional Options The results can be printed or saved using the "Print" and "Done" buttons located at the bottom of the dialog window.
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