Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 260 vinyl? gloves, 70?% leaked viruses. Among 260 latex? gloves, 9?% 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. LOADING... Click the icon to view the technology results. What are the null and alternative? hypotheses? A. Upper H 0?: p 1greater thanp 2 Upper H 1?: p 1equalsp 2 B. Upper H 0?: p 1less thanp 2 Upper H 1?: p 1equalsp 2 C. Upper H 0?: p 1equalsp 2 Upper H 1?: p 1less thanp 2 D. Upper H 0?: p 1equalsp 2 Upper H 1?: p 1greater thanp 2 E. Upper H 0?: p 1not equalsp 2 Upper H 1?: p 1equalsp 2 F. Upper H 0?: p 1equalsp 2 Upper H 1?: p 1not equalsp 2 Identify the test statistic. nothing ?(Round to two decimal places as? needed.) Identify the? P-value. nothing ?(Round to three decimal places as? needed.) What is the conclusion for this? test?

Answer #1

p1(hat)= 0.7

n1= 260

n2= 260

p2(hat)= 0.09

here z test for comparing proportion will be used

claim

H0: p1=p2

Ha: p1>p2

significance level alpha=0.1

pooled sample proportion is

p= 0.395

standard error of the test:

SE= 0.04287

So test statistics will be

z= [p1(hat)-p2(hat)]/SE

=(0.7-0.09)/0.0429

z=14.2273

since this is lower tail test

**p value= p(z>14.2273)=0.000**

Decision making,

p-value <alpha

0.000 <0.1 …… Reject null

there is enough evidence to claim that vinyl gloves have a greater virus leak rate than latex gloves.

............................

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