A pharmaceutical manufacturer is concerned that the mean imp

A pharmaceutical manufacturer is concerned that the mean impurity concentration in pills should not exceed 2%. It is known that impurity concentrations follow a normal distribution with a population standard deviation 0.32%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 2.05%.

What is the sample test statistic (not the critical value) for the hypothesis test that the population mean impurity concentration is 2% or less against its alternative that it is more than 2%?

Solution

          
Getting the test statistic, as              
              
X = sample mean =    2.05          
uo = hypothesized mean =    2          
n = sample size =    64          
s = standard deviation =    0.32          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.25   [ANSWER]