Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among

253253

vinyl​ gloves,

6969​%

leaked viruses. Among

253253

latex​ gloves,

88​%

leaked viruses. Using the accompanying display of the technology​ results, and using a

0.100.10

significance​ level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1.

Answer 1

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Answer:

H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

(b)

n1 = size of sample 1 = 253

p1 = proportion of sample 1= 0.69

n2 = size ofsample 2 = 253

p2 = proportion of sample 2 = 0.08

Р nlpl + n2p2 nl + n2

= 0.385

Q = 1- P = 0.615

SE = PQ(1/n1+1/n2)

= sqrt(0.385*0.615*(2/253)) = 0.0432636

So,

Test statistic is:
Z = (p1 - p2)?SE

= (0.69 - 0.08)/0.0432636 = 14.100

(c)

Table of Area Under Standard Normal Curve gives area = 0.5 nearly

So,

P-value =0 nearly

(d)

The P-value is less than the significancelevel.

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.