Q5 Interpreting Displays.聽In Exerc... [FREE SOLUTION]

Chapter 9: Q5 (page 423)

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.

Expert verified

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.

The output for the test

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:

$H_{0} : p_{1} = p_{2} H_{1} : p_{1} > p_{2}$

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.

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