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 n_{1} = 216

sample proportion of leaked viruses in latex gloves

and sample size for latex golves n_{2} = 216

The test statistic can be written as

which under H_{0} follows a standard normal
distribution.

We reject H_{0} 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 H_{0} 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.

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the icon to view the technology results.

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researchers subjected laboratory gloves to stress. Among 223 vinyl
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and using a 0.10 significance level, test the claim that vinyl
gloves have a greater virus leak rate than latex gloves. Let vinyl
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i need the test statistic and possibly the p-value

A newspaper published an article about a study in which
researchers subjected laboratory gloves to stress. Among 206 vinyl
gloves, 66% leaked viruses. Among 206 latex gloves, 12% leaked
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and using a 0.05 significance level, test the claim that vinyl
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-What are the null and alternative
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-z value
-p-value

A newspaper published an article about a study in which
researchers subjected laboratory gloves to stress. Among 299 vinyl
gloves, 60% leaked viruses. Among 299 latex gloves, 5% leaked
viruses. See the accompanying display of the technology results.
Using a 0.05 significance level, test the claim that vinyl gloves
have a greater virus leak rate than latex gloves. Let vinyl gloves
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(Table at bottom of the question)
Technology results:...

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and using a 0.10 significance? level, test the claim that vinyl
gloves have a greater virus leak rate than latex gloves. Let vinyl
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