A process that produces bottles of shampoo, when operating correctly, produces bottles whose

contents weigh, on average, 20 ounces. A random sample of nine bottles from a single production run

yielded the following content weights (in ounces):

20.4, 19.7, 19.7, 20.6, 20.8, 20.1, 19.7, 20.3, 20.9

Assuming a normal distribution, test the null hypothesis that the process is operating correctly.

Use a two-sided alternative and a 10% significance level.

a. A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not

exceed 3%. Such impurity concentrations follow a normal distribution with a population

standard deviation of 0.4%. A random sample of 64 pills from a production run was checked,

and the population mean impurity concentration was found to be 3.07%.

I. 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%.

II. Suppose that the alternative hypothesis had been two-sided, rather than one-sided, with the null

hypothesis H 0 : = 3%. Test the null at 10% significance level.