SOLUTION: A political polling organization wants to estimate the proportion of independent voters who plan to vote for Candidate X, the incumbent State Senator. Assuming a confidence level o

Question 1193926: A political polling organization wants to estimate the proportion of independent voters who plan to vote for Candidate X, the incumbent State Senator. Assuming a confidence level of 95%, calculate n, the number of voters they need to survey to ensure a 3% margin of error. Calculate n for the following two cases: (1) the organization makes no assumptions based on prior poll results, and (2) based on historical election results, the organization assumes that roughly 62% of eligible voters will vote for Candidate X. (Round your answers upward to the next higher integer.)
(1) If no assumptions are made based on prior poll results, the sample size required to ensure a margin of error of 0.03 is n =
(2) If it is assumed that roughly 62% of eligible voters will vote for Candidate X, the required sample size required to ensure a margin of error of 0.03 is n =

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
error=z(0.975)*sqrt(SE)=1.96*sqrt(0.5*0.5/n)=0.03
square both sides
3.8416*0.25/n=0.0009
n=3.8416*0.25/0.0009=1061.11 or 1068
-
1.96*sqrt(0.62*0.38/n)/=0.03
3.8416*0.2356/n=0.0009
n=1005.65 or 1006
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