Among all U.S. adults, the mean amount of HDL-C (the "good" cholesterol) is 50.7 mg/dL. Researchers are interested in determining if the consumption of black tea can change this mean. A random sample of 28 adults consumed black tea for 6 months, then their cholesterol was measured. The sample produced a mean of 57.9 and standard deviation 13.7. Suppose that mu is the true mean HDL-C for all U.S. adults who consume black tea. We want to test if the true mean is different than 50.7. Use significance level 0.05.

Question 1: What are the null and alternative hypotheses?

Question 2: What is the standardized value of the test statistic?

Question 3: Complete this sentence: At significance level 0.05, we reject H0 if ________.

Question 4: Do we reject the null hypothesis?

Question 5: Based on this hypothesis test, do we conclude consuming black tea alters the mean HDL-C?

Question 6: Should the p-value for this test be greater than or less than the significance level?