Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.1 level that the medicine relieves pain in more than 363 seconds. For a sample of 57 patients, the mean time in which the medicine relieved pain was 367 seconds. Assume the population standard deviation is 24. Find the P-value of the test statistic.

Answer 1

Solution :

=  363

= 367

=24

n = 57

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    =  363

H_a : >  363

Test statistic = z

= ( - ) / / n

= (367 - 363) / / 57

=  1.258

Test statistic = z =  1.26

P(z > 1.26 ) = 1 - P(z < 1.26) =  1 - 0.8962

P-value =0.1038

= 0.01

P-value ≥  

0.1038 ≥ 0.01

The null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is greater than 363, at the 0.01 significance level