A pharmaceutical manufacturer is concerned that the meanimpurity concentration in pills should not excess 2%. It is known that impurity concentrations follow a normal distributionwith a population standard deviation0.32%. A random sampleof 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 2.05%.
a. What is the sample test statistic (not the critical value) for the hypothesis testthat the population mean impurity concentration is 2% or less against its alternative that is more than 2%?
b. Calculate the p-value for this test.
The solution provides a step by step method for hypothesis testing, specifically the calculation of the test statistic and p-value in a given situation.