A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity con- centrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. a. Test at the 5% level the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%. b. Find the p-value for this test. c. Suppose that the alternative hypothesis had been two sided, rather than one-sided. State, without doing the calculations, whether the p-value of the test would be higher than, lower than, or the same as that found in part ii. d. In the context of this problem, explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.
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