Explain minimum sample size to estimate the proportion.
Freshly a case of food poisoning was traced to a particular restaurant chain. The source was identified as well as corrective actions were taken to make sure that the food poisoning would not reoccur. Although the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was led three months after the food poisoning occurred with a sample of 319 patrons contacted. Of the 319 contacted 29 specified that they would not go back to the restaurant because of the potential for food poisoning. What sample size would be wanted in order to be 99% confident that the sample proportion is within .02 of π, the true proportion of customers who refuse to go back to the restaurant?
A. 500
B. 638
C. 1000
D. 1,373
E. 1,777