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%.
a) Test at the 5% level the null hypothesis that the population mean impurity concentration is 2% or less against the alternative that it is more than 2%.
b) Calculate the p-value for this test?