# Question: A pharmaceutical manufacturer is concerned that the impurity concentration in

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%.

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, with the null hypothesis H0: μ = 3. 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 (b). Sketch a graph to illustrate your reasoning.

d. In the context of this problem, explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.

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, with the null hypothesis H0: μ = 3. 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 (b). Sketch a graph to illustrate your reasoning.

d. In the context of this problem, explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.

## Answer to relevant Questions

Test the hypotheses H0: μ ≤ 100 H1: μ > 100 Using a random sample of n = 25, a probability of Type I error equal to 0.05, and the following sample statistics. a. x-bar = 106; s = 15 b. x-bar = 104; s = 10 c. x-bar = 95; ...A random sample of 172 marketing students was asked to rate, on a scale from 1 (not important) to 5 (extremely important), health benefits as a job characteristic. The sample mean rating was 3.31, and the sample standard ...A beer distributor claims that a new display featuring a life-size picture of a well-known rock singer will increase product sales in supermarkets by an average of 50 cases in a week. For a random sample of 20 high-volume ...Of a random sample of 199 auditors, 104 indicated some measure of agreement with this statement: Cash flow is an important indication of profitability. Test at the 10% significance level against a two-sided alternative the ...A random sample of 1,562 undergraduates enrolled in management ethics courses was asked to respond, on a scale from 1 (strongly disagree) to 7 (strongly agree), to this proposition: Senior corporate executives are interested ...Post your question