Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 265 vinyl​ gloves, 57​% leaked viruses. Among 265 latex​ gloves, 5​% 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. LOADING... Click the icon to view the technology results. What are the null and alternative​ hypotheses? A. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 B. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 C. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 D. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 E. Upper H 0​: p 1greater thanp 2 Upper H 1​: p 1equalsp 2 F. Upper H 0​: p 1less thanp 2 Upper H 1​: p 1equalsp 2 Identify the test statistic. 12.94 ​(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? The​ P-value is less than the significance level alpha​, 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.

Answer 1

p1cap = 0.57
p1cap = 0.05
pcap = 0.31

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.57-0.05)/sqrt(0.31*(1-0.31)*(1/265 + 1/265))
z = 12.94

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.