Question

Consider a drug testing company that provides a test for marijuana usage. Among 308 tested? subjects, results from 29 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.

Answer 1

H0: p = 0.10

Ha: p < 0.10

Sample proportion $\hat{p}$ = 29 / 308 = 0.0942

Test statistics

z = $\hat{p}$ - p / sqrt( p (1 - p) / n)

= 0.0942 - 0.10 / sqrt( 0.10 * 0.90 / 308)

= -0.34

This is test statistics value.

Critical value at 0.05 level = -1.645

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim.