Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 271 vinyl gloves, 66% leaked viruses. Among 271 latex gloves, 10% 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.

Answer 1

Let p1 = proportion of vinyl gloves

p2 = proportion of latex gloves

H0: p1 = p2

Ha: p1 > p2

Test statistics

Pooled proportion p* = (x1 + x2 ) / (n1 + n2)

= (0.66 * 271 + 0.10 * 271) / ( 271 + 271)

= 0.38

z = (1 - 2 ) / sqrt [ p* ( 1 - p*) * ( 1 / n1 + 1 / n2) ]

= ( 0.66 - 0.10) / sqrt [ 0.38 * 0.62 * ( 1 / 271 + 1 / 271) ]

= 13.43

Critical value at 0.05 level = 1.645

Since test statisitcs > 1.645, we have sufficient evdidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.