The director of research and development is testing a new dr

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 378 minutes, For a sample of 41 patients, the mean time the drug stayed in the system was 374 minutes. Assume the variance is known to be 625.

Solution

ans)
Test H0 : New drug stays in the system >= 378 minutes ag. H1: New drug stays in the system < 378 mins!

variance is known for population = 625..i.e, s.d = sqrt ( 625) = 25..
sample mean = 374 and sample size =n= 41....

test statistic = ( sample mean - population mean ) / ( s.d / sqrt (n) )
= ( 374 - 378 ) / ( 25 / sqrt ( 41) ) = -1.0245.......
p-value = 0.1527996......
p-value is > 0.02 which is the significance level!..
so, accept H0!
There is no evidence that the drug stays in the system for less than 378 minutes!