### Technology Results**Statistical Analysis Summary:**- **Pooled Proportion**: 0.34 - The pooled proportion is a weighted average of proportions from two different samples, in this case, yielding 0.34.- **Test Statistic, $ z $**: 10.2947 - The $ z $-value of 10.2947 indicates the number of standard deviations the test statistic is from the mean under the null hypothesis.- **Critical $ z $**: 1.2816 - The critical $ z $-value of 1.2816 is the threshold above which the $ z $-value must fall to conclude that the observed effect is statistically significant at the chosen confidence level (typically 80%).- **P-value**: 0.0000 - A P-value of 0.0000 indicates very strong evidence against the null hypothesis, suggesting that the observed result is highly significant.- **80% Confidence Interval**: \[ 0.3862473 < p_1 - p_2 < 0.4822786 \] - This interval provides a range within which the true difference between proportions ( $ p_1 - p_2 $ ) lies with 80% confidence.**Statistical Hypothesis Summary:**- Null Hypothesis ($ H_0 $): $ p_1 = p_2 $- Alternative Hypothesis ($ H_1 $): $ p_1 \neq p_2 $The information displays results from a statistical test comparing two proportions. The very low P-value suggests rejecting the null hypothesis in favor of the alternative hypothesis with high confidence. Buttons:- **Print**: Initiates printing of the displayed results.- **Done**: Closes the results window.### ExplanationThe result dialog provides key statistics for interpreting a hypothesis test comparing two proportions. For an educational purpose, students and researchers can use this information to understand the strength and significance of their evidence and make informed conclusions based on the data and statistical outputs. ### Study on Virus Leak Rates of Laboratory GlovesA newspaper published an article about a study in which researchers subjected laboratory gloves to stress tests to observe virus leakage rates. Among 251 vinyl gloves tested, 55% leaked viruses. Among 251 latex gloves tested, 12% leaked viruses. The goal is to test, at a 0.10 significance level, the claim that vinyl gloves have a greater virus leak rate than latex gloves. Assume that vinyl gloves are treated as population 1.**Click the icon to view the technology results.**#### Hypothesis Testing**What are the null and alternative hypotheses?**- **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 = 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 \neq p_2 $**Identify the test statistic.**\[ \Box \]*(Round to two decimal places as needed.)***Identify the P-value.**\[ \Box \]*(Round to three decimal places as needed.)***Conclusion for the test:**The P-value is \[ \Underline{\hspace{30px}} \] the significance level $\alpha$, so \[ \SelectorArrow{\hspace{30px}} \] the null hypothesis. There is \[ \SelectorArrow{\hspace{30px}} \] evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Answered: A newspaper published an article about…

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 newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 262 vinyl gloves, 68% leaked viruses. Among 262 latex gloves, 11% 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. Click the icon to view the technology results. What are the null and alternative hypotheses? O A. Ho: P1 P2 H₁: P1 P2 OD. Ho: P1 P2 H₁: P1 = P2 Identify the test statistic. B. (Round to two decimal places as needed) Ho: P1 P2 H₁: P1 = P2 O E. Ho: P1 P2 H₁: P1 P2 OC. Ho: P1 P2 H₁: P1 = P2 OF. Ho: P1 = P2 H₁: P1 P2
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