Question

Consider a drug testing company that provides a test for marijuana usage. Among 257 tested subjects, results from 28 subjects were wrong (either a false positive or a false negative). 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. ( Round to two decimal places as needed )

Identify the P-value for this hypothesis test. ( Round to three decimal places as needed)

Identify the conclusion for this hypothesis test.

A.Fail to reject Upper H 0. There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

B.Reject Upper H 0. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

C.Reject Upper H 0.There is sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

D.Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p < 0.10

= x / n = 28 / 257 = 0.1089

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1089 - 0.10 / [(0.10 * 0.90) / 257]

= 0.48

P(z < 0.48) = 0.6844

P-value = 0.684

= 0.05

P-value >

Fail to reject the null hypothesis .

D.Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.