A drug company manufactures pain pills each with a pharmaceutical content of 3000 g. The process population variance of the pill concentration is known to be 800 g^2 . During quality control, 20 sample pills are collected and show the sample mean to be 3012 g.

a) Is there good evidence to say the sample mean is not the target value of 3000 g? Use an = 0.05 and make all necessary assumptions and state your hypotheses

b) What is the type 2 error probability if the true mean is 2980 g?