Question

The company Drug Test Success provides a "1-Panel-THC" test for marihuana usage. Among 300 tested subjects, results from 27 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% of the test results are wrong

Answer 1

There is evidence for the claim that less than 10% of the test results are wrong

Explanation:

Given that the company Drug Test Success provides a "1-Panel-THC" test for marihuana usage.

Among 300 tested subjects, results from 27 subjects were wrong (either a false positive or a false negative.)

Sample proportion =
`(27)/(300) \\=0.09`

H0: p = 0.10

Ha: p <0.10

(left tailed test)

p difference = 0.09-0.10 = -0.01

Std error =
`√(0.1*0.9/300) \\=0.005196`

z statistic = -1.9245

p value = 0.027

Since p <0.05 we reject H0

There is evidence for the claim that less than 10% of the test results are wrong