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Chapter 9: Q5BSC (page 414)

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

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.

Step by step solution

01

Given information

The output for the test

02

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:

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

03

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.

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Most popular questions from this chapter

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\({\bf{E = }}{{\bf{z}}_{\frac{{\bf{\alpha }}}{{\bf{2}}}}}\sqrt {\frac{{{{\bf{p}}_{\bf{1}}}{{\bf{q}}_{\bf{1}}}}}{{{{\bf{n}}_{\bf{1}}}}}{\bf{ + }}\frac{{{{\bf{p}}_{\bf{2}}}{{\bf{q}}_{\bf{2}}}}}{{{{\bf{n}}_{\bf{2}}}}}} \)

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\({\bf{n = }}\frac{{{\bf{z}}_{\frac{{\bf{\alpha }}}{{\bf{2}}}}^{\bf{2}}}}{{{\bf{2}}{{\bf{E}}^{\bf{2}}}}}\)

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