Question

Consider a drug testing company that provides a test for marijuana usage. Among 280 tested​ subjects, results from 25 subjects were wrong​ (either a false positive or a false​ negative). Use a 0.01 significance level to test 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

n = 280

x = 25

= x / n = 25 / 280 = 0.0893

P₀ = 0.10

1 - P₀ = 1 - 0.10 = 0.90

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0893 - 0.10 / [(0.10 * 0.90) / 280]

= -0.598

Test statistic = -0.598

P(z < -0.598) = 0.2749

P-value = 0.2749

= 0.01

P-value >

Fail to reject the null hypothesis .

There is no evidence that claim that less than 10 percent of the test results are wrong .