In a survey reported in a special edition of Newsweek (Spring/Summer 1999, Health for Life), only 3% of a sample of 757 American women responded "Not at all satisfied" to the question, "How satisfied are you with your overall physical appearance?"

a. The margin of error for the poll was reported as 3.5%. Use the conservative approximation for margin of error to verify that this is roughly correct.

b. On the basis of the reported margin of error, calculate a 95% confidence interval for the percentage of all American women who are "not at all satisfied" with their physical appearance. Are all values in this interval valid estimates of the population percentage? Explain.

c. Use the more precise formula to calculate the margin of error.

d. On the basis of the margin of error in part (c), calculate a 95% confidence interval for the population percentage. Write a sentence that interprets this confidence interval for somebody who knows little about statistics.