Question

Consider a drug testing company that provides a test for marijuana usage. Among

287

tested​ subjects, results from

26

subjects were wrong​ (either a false positive or a false​ negative). Use a

0.10

significance level to test the claim that less than

10

percent of the test results are wrong.

Answer 1

Solution :

Given that ,

n = 287

x = 26

The null and alternative hypothesis is ,

H0 : p = 0.10

Ha : p < 0.10

This is the left tailed test .

= x / n = 26 / 287 = 0.0906

P0 = 10 % = 0.10

1 - P0 = 1-0.10 = 0.90

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.0906 - 0.10 / [0.10 ( 1 - 0.10) / 287 ]

= -0.531

The test statistic = -0.531

P-value = 02976.

= 0.10

0.2976 > 0.10

P-value >  

Fail to reject the null hypothesis .

There is not sufficient evidence to test the claim .