A plot of 75 voters found that 30 of them voted in the last election How many voters must be sampled to constructa 99% interval with a margin of error equal to 0.057 Zertical value at 99% is 2.58 n=hat (p)hat (q)((Z_(c))/(E))^2 640 sza 42% sso

To construct a 99% confidence interval with a margin of error equal to 0.057, we need to determine the sample size required.<br /><br />Given information:<br />- Sample size (n) = 75<br />- Proportion of voters who voted in the last election (p) = 30/75 = 0.4<br />- Margin of error (E) = 0.057<br />- Z-value at 99% confidence level (Zc) = 2.58<br /><br />The formula to calculate the sample size is:<br />n = (p * q * (Zc/E)^2)<br /><br />Where:<br />- p is the proportion of voters who voted in the last election (0.4)<br />- q is the proportion of voters who did not vote in the last election (1 - p = 0.6)<br />- Zc is the Z-value at the desired confidence level (2.58)<br />- E is the desired margin of error (0.057)<br /><br />Plugging in the values, we get:<br />n = (0.4 * 0.6 * (2.58/0.057)^2)<br />n = (0.24 * (45.16)^2)<br />n = (0.24 * 2042.56)<br />n = 490.42<br /><br />Rounding up to the nearest whole number, the required sample size is 491.<br /><br />Therefore, to construct a 99% confidence interval with a margin of error equal to 0.057, a sample size of 491 voters must be sampled.