Question

Interpreting Displays.

In Exercises 5 and 6, use the results from the given displays.

Testing Laboratory Gloves, The New York Times published an article about a study by Professor Denise Korniewicz, and Johns Hopkins researched subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses; among 240 latex gloves, 7% leaked viruses. See the accompanying display of the Statdisk results. Using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Short answer

Reject the null hypothesis under 0.01 significance level.

There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Step-by-step solution

Given information

The output for the test

Describe the hypothesis to be tested.

Let\({p_1}\)be the population proportion of virus leak rate of vinyl gloves and\({p_2}\)be population proportion of virus leak rate of latex gloves.

Mathematically, the test hypothesis is:

\(\begin{array}{l}{H_0}:{p_1} = {p_2}{\rm{ }}\\{H_1}:{p_1} > {p_2}\end{array}\)

State the result

From the output the p-value is 0.0000.

Decision rule:

If the p-value is smaller than 0.01, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

As the p-value is lesser than 0.01, reject the null hypothesis.

Thus, there is enough evidence to conclude that the leak rate is greater in vinyl gloves than latex.