Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 398 seconds. For a sample of 96 patients, the mean time in which the medicine relieved pain was 404 seconds. Assume the population standard deviation is 22 . Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 398

H_a :    < 398

= 404

= 398

= 22

n = 96

Test statistic = z

= ( - ) / / n

= (404 - 398 ) / 22 / 96

= 2.67

Test statistic = 2.67

P(z >) = 1 - P(z < 2.67 ) = 1 - 0.9962 = 0.0038

P-value = 0.0038