**Study on Laboratory Gloves and Virus Leakage**A newspaper article published a study involving laboratory gloves subjected to stress testing. The study involved:- **237 vinyl gloves:** 59% of these gloves leaked viruses.- **237 latex gloves:** 9% of these gloves leaked viruses.The study aimed to test the claim, at a 0.05 significance level, that vinyl gloves have a higher virus leak rate than latex gloves. For this analysis, vinyl gloves are considered as population 1.**Hypotheses:**- Null Hypothesis (H₀): $ p_1 = p_2 $- Alternative Hypothesis (H₁): $ p_1 > p_2 $**Statistical Analysis:**- **Pooled proportion:** 0.34- **Test statistic (z):** 11.4166- **Critical z-value:** 1.6449- **P-value:** 0.0000**Confidence Interval:**The 90% confidence interval for the difference in proportions is given as $ 0.437413 < p_1 - p_2 < 0.558632 $.The analysis strongly supports the claim that vinyl gloves have a higher virus leak rate than latex gloves, with the p-value indicating a significant difference in leak rates.

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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 237 vinyl gloves, 70% leaked viruses. Among 237 latex gloves, 7% leaked viruses. Using the accompanying display of the technology results, and using a 0.05 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. What are the null and alternative hypotheses? Identify the test statistic. (round to two decimal places as needed) Identify the P-value. (round to four decimal places as needed) What is the conclusion for this test? The P-value is ___________ ( less than/greater than) the significance level α, so __________ ( reject/fail to reject) the null hypothesis. There is ________ ( sufficient/insufficient) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

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