A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 276 vinyl gloves, 68% leaked viruses. Among 276 latex gloves, 15% leaked viruses. Using the accompanying display of the technology results, and using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. i Click the icon to view the technology results. What are the null and alternative hypotheses? O A. Ho: P, > P2 H: P1 = P2 O B. Ho: P, + p2 H: P1 =P2 OC. Ho: P1 =P2 H: P, +P2 OF. Ho: P1 =P2 H:P1 > P2 O D. Ho: P1
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 276 vinyl gloves, 68% leaked viruses. Among 276 latex gloves, 15% leaked viruses. Using the accompanying display of the technology results, and using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. i Click the icon to view the technology results. What are the null and alternative hypotheses? O A. Ho: P, > P2 H: P1 = P2 O B. Ho: P, + p2 H: P1 =P2 OC. Ho: P1 =P2 H: P, +P2 OF. Ho: P1 =P2 H:P1 > P2 O D. Ho: P1
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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Answer please and thank you.
![**Research Study on Laboratory Gloves and Virus Leak Rates**
A newspaper article reported on a study wherein researchers tested laboratory gloves for virus leakage under stress conditions. The study details are as follows:
- **Vinyl Gloves**: Out of 276 gloves tested, 68% showed virus leakage.
- **Latex Gloves**: Out of 276 gloves tested, 15% showed virus leakage.
The objective is to test, at a 0.10 significance level, whether vinyl gloves have a higher virus leak rate compared to latex gloves. For this study, vinyl gloves are considered as population 1.
### Null and Alternative Hypotheses
Participants must choose from the following options:
- **Option A**: \( H_0: p_1 > p_2 \) | \( H_1: p_1 = p_2 \)
- **Option B**: \( H_0: p_1 \neq p_2 \) | \( H_1: p_1 = p_2 \)
- **Option C**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 \neq p_2 \)
- **Option D**: \( H_0: p_1 < p_2 \) | \( H_1: p_1 = p_2 \)
- **Option E**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 < p_2 \)
- **Option F**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 > p_2 \)
### Test Statistic and P-Value Identification
- **Identify the Test Statistic**: Input should be rounded to two decimal places.
- **Identify the P-Value**: Input should be rounded to three decimal places.
### Conclusion of the Test
Fill in the following framework based on the findings:
- The P-value is [Value] the significance level \(\alpha\), so [Decision on Null Hypothesis] the null hypothesis. There is [Strength of Evidence] evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
This study aims to provide insights into the effectiveness of different glove materials in preventing virus transmission in laboratory settings.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f0fb466-9e5e-42c4-aac7-4119dc8b6f62%2F45921e45-863e-4468-9fb2-6062410957d8%2Fn3qkljj_processed.png&w=3840&q=75)
Transcribed Image Text:**Research Study on Laboratory Gloves and Virus Leak Rates**
A newspaper article reported on a study wherein researchers tested laboratory gloves for virus leakage under stress conditions. The study details are as follows:
- **Vinyl Gloves**: Out of 276 gloves tested, 68% showed virus leakage.
- **Latex Gloves**: Out of 276 gloves tested, 15% showed virus leakage.
The objective is to test, at a 0.10 significance level, whether vinyl gloves have a higher virus leak rate compared to latex gloves. For this study, vinyl gloves are considered as population 1.
### Null and Alternative Hypotheses
Participants must choose from the following options:
- **Option A**: \( H_0: p_1 > p_2 \) | \( H_1: p_1 = p_2 \)
- **Option B**: \( H_0: p_1 \neq p_2 \) | \( H_1: p_1 = p_2 \)
- **Option C**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 \neq p_2 \)
- **Option D**: \( H_0: p_1 < p_2 \) | \( H_1: p_1 = p_2 \)
- **Option E**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 < p_2 \)
- **Option F**: \( H_0: p_1 = p_2 \) | \( H_1: p_1 > p_2 \)
### Test Statistic and P-Value Identification
- **Identify the Test Statistic**: Input should be rounded to two decimal places.
- **Identify the P-Value**: Input should be rounded to three decimal places.
### Conclusion of the Test
Fill in the following framework based on the findings:
- The P-value is [Value] the significance level \(\alpha\), so [Decision on Null Hypothesis] the null hypothesis. There is [Strength of Evidence] evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
This study aims to provide insights into the effectiveness of different glove materials in preventing virus transmission in laboratory settings.
![**Technology Results**
- **Pooled proportion**: 0.41
- **Test statistic, z**: 12.6207
- **Critical z**: 1.2816
- **P-value**: 0.0000
**80% Confidence Interval**:
\[ 0.4836782 < p_1 - p_2 < 0.5742929 \]
This section presents the statistical analysis results, including the pooled proportion, test statistic, critical value, and p-value. It also provides an 80% confidence interval for the difference in proportions \( p_1 - p_2 \). A low p-value indicates strong evidence against the null hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f0fb466-9e5e-42c4-aac7-4119dc8b6f62%2F45921e45-863e-4468-9fb2-6062410957d8%2Fik559ej_processed.png&w=3840&q=75)
Transcribed Image Text:**Technology Results**
- **Pooled proportion**: 0.41
- **Test statistic, z**: 12.6207
- **Critical z**: 1.2816
- **P-value**: 0.0000
**80% Confidence Interval**:
\[ 0.4836782 < p_1 - p_2 < 0.5742929 \]
This section presents the statistical analysis results, including the pooled proportion, test statistic, critical value, and p-value. It also provides an 80% confidence interval for the difference in proportions \( p_1 - p_2 \). A low p-value indicates strong evidence against the null hypothesis.
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