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 concentrations 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%. 1. Find the p-value for this test. 2. Suppose that the alternative hypothesis had been two-sided, rather than one-sided, with the null hypothesis H0 : µ = 3. State, without doing the calculations, whether the value of the test would be higher than, lower than, or the same as that found in part (1). Sketch a graph to illustrate your reasoning.
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 concentrations follow a
1. Find the p-value for this test.
2. Suppose that the alternative hypothesis had been two-sided, rather than one-sided, with the null hypothesis H0 : µ = 3. State, without doing the calculations, whether the value of the test would be higher than, lower than, or the same as that found in part (1). Sketch a graph to illustrate your reasoning.
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