Question

Consider a drug testing company that provides a test for marijuana usage. Among 305 tested subjects, results from 26 subjects were wrong (either false positive or a false negative) Use a .5 significance level to test the claim that less than 10% of the test results are wrong. Identify the test statistic and the P value for this hypothesis test.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 0.085

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.10

Ha: p < 0.10

Test statistics

z = ( - ) / *(1-) / n

= ( 0.085 - 0.10) / (0.10*0.90) /305

= -0.873

P-value = P(Z < z )

= P(Z < -0.873 )

= 0.1913

The p-value is p = 0.1913, and since p = 0.1913 < 0.5, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to claim that less than 10% of the test results are wrong.