Question

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 327 minutes. For a sample of 67 patients, the mean time the drug stayed in the system was 330 minutes. Assume the population variance is known to be 529. Determine the test-z and make a decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 327

H_a : > 327

Test statistic = z

= ( - ) / / n

= (330 - 327 ) /23 / 67

= 1.07

Test statistic = 1.07

P(z > 1.07) = 1 - P(z < 1.07) = 1 - 0.8577 = 0.1423

P-value = 0.1423

= 0.01

P-value >

Fail to reject the null hypothesis .