Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 340 seconds. For a sample of 53 patients, the mean time in which the medicine relieved pain was 347 seconds. Assume the population standard deviation is 18. Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 340 seconds

Hypothesized mean : = 340 seconds

Null hypothesis : H_o : =

She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 340 seconds

Therefore,

Alternate hypothesis :H₁: >

Right tailed test:

As population standard deviation is known, Z-test is appropriate

Given
Sample Mean : mean time in which the medicine relieved pain	347
Population Standard Deviation :	18
Sample Size : n	53
Level of significance :	0.02

For Right tailed test:

p-value = 0.0023