The mayor of a small town would like to know whether a local bond issue is likely to pass or not. He mails a survey to 500 randomly selected voters. How many returns must he get in order to know the proportion that will support the bond issue within an error of 5% and a confidence level of 95%? If he gets a 60% return from the mailing and would like to keep the error at 5%, what will happen to his confidence in the result? If he gets a 60% return from the mailing and would like to maintain his 95% confidence in the result, what will happen to the error?
In every case, we use the relation n = p * q * (z/E)^2 = p * (1 - p) * (z/E)^2
(a) n = 0.5 * 0.5 * ...
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