5) In a recent presidential election, 500 voters were surveyed and 350 of them said that...
5) In a recent presidential election, 500 voters were surveyed and 350 of them said that they voted for the candidate who won.
a. Construct a 96% confidence interval estimate of the percentage of voters who said they voted for the candidate who won.
b. How many voters must they survey if they want 90% confidence that the sample proportion is in error by no more than 0.02?
Homework Answers
p = 350/500 = 0.70
a)
z value at 96% = 2.0537
CI = p +/- z *sqrt(p*(1-p)/n)
= 0.70 +/- 2.0537 * sqrt(0.70*(1-0.70)/500)
=0.70 +/- 0.0421
= (0.6579 , 0.7421 )
b)
z value at 90% = 1.645
ME = 0.02
ME = z *sqrt(p*(1-p)/n)
n = (1.645/0.02)^2 * 0.70 *(1-0.70)
n = 1420
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