Question #3A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 298 vinyl gloves, 60% leaked viruses. Among 298 latex gloves,13% leaked viruses. Using the accompanying display of the technology results, and using a0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. View the technology results.Technology resultsPooled proportion: 0.37 Test statistic, z: 11.9063 Critical z: 2.3264 P-value: 0.0000 98% Confidence interval:0.3896624 < p1 − p2 < 0.5499349 What are the null and alternative hypotheses? A. H0: p1 = p2 H1: p1 < p2B. H0: p1 = p2 H1: p1 ≠ p2C. H0: p1 > p2 H1: p1 = p2D. H0: p1 < p2 H1: p1 = p2E. H0: p1 = p2 H1: p1 > p2F. H0: p1 ≠ p2 H1: p1 = p2 Identify the test statistic. ___________(Round to two decimal places as needed.) Identify the P-value. __________(Round to three decimal places as needed.) What is the conclusion for this test? The P-value is ___________ ( A. less than, B. greater than ) the significance level of α,so ____________ ( A. fail to reject, B. reject ) the null hypothesis. There is ___________ ( A. insufficient, B. sufficient ) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Given : Pooled proportion: 0.37 Test statistic, z: 11.9063 Critical z: 2.3264 P-value: 0.0000 98% Confidence interval: 0.3896624 < p1 − p2 < 0.5499349 Solution : a) Claim : The vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Hypothesis test : The null and alternative hypothesis is H0: p1 = p2 H1: p1 > p2b) Test statistic is z = 11.91C) P-value = 0.000D) Decision rule : Reject Ho if P-value ≤ significance level α, otherwise fail to reject. The P-value is less than the significance level of α, so reject the null hypothesis. There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

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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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Question #3

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 298 vinyl gloves, 60% leaked viruses. Among 298 latex gloves,

13% 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.

View the technology results.

Technology results

Pooled proportion: 0.37

Test statistic, z: 11.9063

Critical z: 2.3264

P-value: 0.0000

98% Confidence interval:

0.3896624 < p₁ − p₂ < 0.5499349

What are the null and alternative hypotheses?

A. H₀: p₁ = p₂

H₁: p₁ < p₂

B. H₀: p₁ = p₂

H₁: p₁ ≠ p₂

C. H₀: p₁ > p₂

H₁: p₁ = p₂

D. H₀: p₁ < p₂

H₁: p₁ = p₂

E. H₀: p₁ = p₂

H₁: p₁ > p₂

F. H₀: p₁ ≠ p₂

H₁: p₁ = p₂

Identify the test statistic.

___________

(Round to two decimal places as needed.)

Identify the P-value.

__________

(Round to three decimal places as needed.)

What is the conclusion for this test?

The P-value is ___________ ( A. less than, B. greater than ) the significance level of α,

so ____________ ( A. fail to reject, B. reject ) the null hypothesis. There is ___________ ( A. insufficient, B. sufficient ) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

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