Death penalty: A group claims that the overall feelings of the general population on the death penalty is changing. 643 people were interviewed, and of them, 258 believed in using the death penalty. Construct a 95% confidence interval for the proportion of people that believe in the death penalty. Follow the steps below: Find E: (round to 3 decimal places)

The objective of this question is to construct a 95% confidence interval for the proportion of people that believe in the death penalty. The first step in this process is to find the margin of error (E).The formula for the margin of error (E) in a confidence interval for a proportion is E = Z * sqrt[(p(1 - p) / n)], where Z is the Z-score, p is the sample proportion, and n is the sample size.In this case, the sample size (n) is 643, the sample proportion (p) is 258/643 = 0.401, and the Z-score for a 95% confidence interval is approximately 1.96 (this value is found in a standard Z-table).Substituting these values into the formula gives E = 1.96 * sqrt[(0.401(1 - 0.401) / 643)].To simplify this, first calculate the value inside the square root: 0.401(1 - 0.401) / 643 = 0.000239.Then, take the square root of this value: sqrt(0.000239) = 0.015.Finally, multiply this by the Z-score: 1.96 * 0.015 = 0.029.Therefore, the margin of error (E) is 0.029, or 2.9%, when rounded to three decimal places.The margin of error (E) for a 95% confidence interval for the proportion of people that believe in the death penalty, based on a sample of 643 people of which 258 believe in the death penalty, is approximately 0.029 or 2.9%.