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 352 minutes. For a sample of 64 patients, the mean time the drug stayed in the system was 356 minutes. Assume the population variance is known to be 324. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 352

Ha: 352

The test statistics,

Z =( - )/ (/n)

= ( 356 - 352 ) / ( 18 / 64 )

= 1.78

P-value = P(Z > z)

= 1 - P(Z < 1.78 )

= 0.0377

Since, P-value = 0.0377 > 0.01, It is concluded that fail to reject the null hypothesis.