8.105 Healthy Eating Don't Americans know that eating pizza and french fries leads to being overweight? In an American Demographics article23, a survey of women who are the main meal preparers in their house- holds reported these results: 90% know that obesity causes health problems. 80% know that high fat intake may lead to health problems. 86% know that cholesterol is a health problem. 88% know that sodium may have negative effects on health.

a. Suppose that this survey was based on a random sample of 750 women. How accurate do you expect the percentages given above to be in estimating the actual population percentages? (HINT: If these are the only four percentages for which you need a margin of error, a conservative estimate for p is p = 0.80.)

b. If you want to decrease your sampling error to 1%, how large a sample should you take?