Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 225 vinyl? gloves, 60?% leaked viruses. Among 225 latex? gloves, 9?% 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. Let vinyl gloves be population 1.

Technology Results:::

Pooled? proportion: 0.35

Test? statistic, z: 11.2921

Critical? z: 1.6449

?P-value: 0.0000

90?% Confidence? interval:

0.4441890 < p1? p2 <0.5691444

A) What are the null and alternative hypotheses?

B) Identify the test statistic

C) Identify the P-value

D) What is the conclusion for the test?

Answer 1

Let vinyl gloves be population 1 and latex gloves be population 2.

Let n₁ = sample size of population 1 = 225

n₂ = sample size of population 2 =225

p₁ = sample proportion of virus leak among population 1 = 0.6

p₂ = sample proportion of virus leak among population 2 = 0.09

A)

Now we have to test the claim that vinyl gloves have a greater virus leak rate than latex gloves.

That means we have to test that the proportion of virus leak among population 1 is greater than the proportion of virus leak among the population 2. Therefore, the hypothesis is,

B)

Now, the test statistic for testing the above hypothesis is,

where, p₁ = sample proportion of population 1, p₂ = sample proportion of population 2,

Therefore, the pooled proportion P is,

And the test statistic is,

c)

Now the p-value is

p-value = P(Z>11.3411) = 0.0000

D)

Level of significance = 0.05

Since p-value < level of significance, therefore we reject the null hypothesis H₀ and conclude that there is evidence that vinyl gloves have a greater virus leak rate than latex gloves at 5% level of significance.