A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c).   (a) What sample size should be obtained if he wants to be within 3 percentage points with 96​% confidence if he uses an estimate of 48​% obtained from a​ poll?   (b) What sample size should be obtained if he wants to be within 3 percentage points with 96% confidence if he does not use any prior estimates?   (c) Why are the results from parts (a) and (b) so close?

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A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c).
 
(a) What sample size should be obtained if he wants to be within
3 percentage points with 96​% confidence if he uses an estimate of 48​% obtained from a​ poll?
 
(b) What sample size should be obtained if he wants to be within 3 percentage points with 96% confidence if he does not use any prior estimates?
 
(c) Why are the results from parts (a) and (b) so close?
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