Mathematics: Consider a drug testing company that provides a test for marijuana usage. Among 317 tested subjects, results from 25 subjects were wrong (either a false positive or a falsenegative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pless than 0.10.1 B. Upper H 0H0: pless than 0.10.1 Upper H 1H1: pequals=0.10.1

Because of the size of the numbers the bigger the numbers the bigger the sum...

Consider a drug testing company that provides a

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26.01.2022

The null and alternative hypothesis are:

$H_0: \pi=0.1\\\\H_a:\pi$

The test statistic for this hypothesis test is z=-1.15.

The P-value for this hypothesis test is P-value=0.124.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that less than 10 percent of the test results are wrong.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.1\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=317.

The sample proportion is p=0.079.

p=X/n=25/317=0.079

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{317}}\\\\\\ \sigma_p=\sqrt{0.000284}=0.017$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.079-0.1+0.5/317}{0.017}=\dfrac{-0.019}{0.017}=-1.153$

This test is a left-tailed test, so the P-value for this test is calculated as:

P-value=P(z

As the P-value (0.124) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

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