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A pharmaceutical company is concerned that the impurity concentration in pills does not exceed 2%. It is known that from a particular production run, impurity concentrations follow a normal distribution with standard deviation 0.3%. A random simple of 64 pills from a production run was checked and the sample mean impurity concentration was found to be 2.06%.
a)Test at the 5% level the null hypothesis that the population mean impurity concentration is 3%.
b)Find the probability of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 2.10%.