Question

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

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.

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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.