The average serum cholesterol level in a certain group of patients is 240 milligrams. A new medication is designed to lower the cholesterol level in this population after one month. A sample of 60 people in the population used the medication for 30 days, after which their average cholesterol level was 232 milligrams with a standard deviation of 18 milligrams. The manufacturer of the new medication would like to see if the average cholesterol level in the population has been reduced.

1. Using statistical notation, specify the appropriate null and alternative hypotheses.

2. Calculate the p-value for the hypothesis test.

3. Make a decision, "reject" or "do not reject," at the a = 0.05 level. Explain your reasoning.

4. Based on the decision you made in question #7, what type of error might you have made?

5. Calculate a 95% confidence interval for µ, the average serum cholesterol level in the population after one month.