Question: A survery of college students was taken to determine what percentage of students would be voting in the upcoming elections. The results were stated as 66% with a margin of error of plus/minus 5%. What is meant by plus/minus 5%?

a)In the sample, the percentage of college students who plan to vote is between 61% and 71%
b) The percentage of the entire population of college students who plan to vote in the upcoming elections is between 61% and 71%
c) It is unlikely that the given sample propotion would be obtained unless the true percentage of college students who planned to vote in the upcoming elections was between 61% and 71%
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Answer: Ans:
a) mean=0.66 ,
margin of error, e=sd/sqrt(n)*z_c=standard error*critical z=0.05
standard error=0.05/1.96 [critical z at 95% confidence.]=0.025

x bar=0.61 , the z= (0.61-0.66)/0.025=-2
x bar=0.71 , the z= (0.71-0.66)/0.025=+2

P(0.61 =P(-2 =0.4772+0.4772
=0.9544=95.44%(Ans.)  Edit