Refer to Exercise 12.53.

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

b. Obtain a sample size that will ensure a margin of error of at most 1.5 percentage points for a 99% confidence interval without making a guess for the observed value of p̂.

c. Find a 99% confidence interval for p if, for a sample of the size determined in part (b), 82.2% of the registered voters sampled favor the creation of standards on CAFO pollution and, in general, view CAFOs unfavorably.

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 registered voters sampled who favor the creation of standards on CAFO pollution and, in general, view CAFOs unfavorably will be between 75% and 85%.

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