Question

There are 20,000 eligible voters in York County, South Carolina. A random sample of 500 York County voters revealed 350 plan to vote to return Louella Miller to the state senate.

a.	Construct a 99% confidence interval for the proportion of voters in the county who plan to vote for Ms. Miller. (Round your answers to 3 decimal places)

Confidence interval for the proportion is.............. and ...................

Answer 1

P = 350/500 = 0.7

Between 0.648 and 0.752, found by

$7\pm 2.58\left ( \sqrt{\frac{0.7(1-0.7)}{500}} \right )\left ( \sqrt{\frac{20000-500}{20000-1}} \right )$.

Yes, because even the lower limit of the confidence interval is above 0.500.

Answer 2

Sample statistic = p = 350/500 = 0.7

Standard error = sqrt(p*(1p)/n) = sqrt(07*03/500) = 0.021

For 99% Confidence Interval, the multiplier to be used = 2.58

Therefore, Confidence Interval would become ( 0.7 - 0.021*2.58 , 0.7 + 0.021*2.58) = (0.646 , 0.754)