Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 216 vinyl​ gloves, 64​% leaked viruses. Among 216 latex​ gloves, 99​% 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.

Identify the test statistic.

Answer 1

Let denotes the true proportion of leaked viruses for vinyl and latex gloves respectively.

To test the claim that  vinyl gloves have a greater virus leak rate than latex gloves,

i.e. to test against

Here

sample proportion of leaked viruses in vinyl​ gloves

and sample size for vinyl golves n₁ = 216

sample proportion of leaked viruses in latex​ gloves

and sample size for latex golves n₂ = 216

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 1% level of significance if P-value < 0.01

Now,

The value of the test statistic =

P-value

Since P-value > 0.05, so we fail to reject H₀ at 1% level of significance and we can conclude that there is insufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.