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 less than 314 seconds. For a sample of 53 patients, the mean time in which the medicine relieved pain was 310 seconds. Assume the standard deviation is known to be 19. Perform the hypotheses test to check the claim.

Answer 1

Solution :

Given that,

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 314

Ha: 314

The test statistics,

Z =( - )/ (/n)

= ( 310 - 314 ) / ( 19 / 53 )

= -1.53

P-value = P( Z < z )

= P(Z < -1.53)

= 0.0630

The p-value is p = 0.0630, and since p = 0.0630 > 0.02, it is concluded that fail to reject the null hypothesis.

There is no evidence at the 0.02 level that the medicine relieves pain in less than 314 seconds.