Refer to Exercise 12.52.

a. Find the margin of error for the estimate of p.

b. Obtain a sample size that will ensure a margin of error of at most 0.02 for a 95% confidence interval without making a guess for the observed value of p̂.

c. Find a 95% confidence interval for p if, for a sample of the size determined in part (b), 36.0% of those sampled drink alcoholic beverages at least once a week.

d. Determine the margin of error for the estimate in part (c) and compare it to the margin of error specified in part (b).

e. Repeat parts (b)-(d) if you can reasonably presume that the percentage of adults sampled who drink alcoholic beverages at least once a week will be at most 40%.

f. Compare the results you obtained in parts (b)-(d) with those obtained in part (e).