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

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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

Answer 1

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

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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

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