Final answer:
To estimate the proportion of U.S. voters who oppose capital punishment, with a 95% confidence level and a 2% margin of error, a pollster should survey at least 2401 voters using a worst-case population proportion estimation of 0.50.
Step-by-step explanation:
To determine the necessary sample size a pollster would need to estimate the true proportion of U.S. voters who oppose capital punishment within a 2% margin of error at a 95% confidence level, a formula based on the Z-score for the desired confidence level, the estimated population proportion, and the desired margin of error is used. The 'worst case scenario' for the population proportion (p) used in the calculation is 0.50, as it provides the maximum variance and hence the largest required sample size. Using the formula n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to a 95% confidence level (1.96), p is the estimated population proportion (0.50 for worst case scenario), and E is the desired margin of error (0.02), we can calculate the necessary sample size. Therefore, the smallest number of voters needed would be calculated as follows: n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2. Calculating this, we get n = (3.8416 * 0.25) / 0.0004, which equals 2401. Thus, a minimum sample size of 2401 voters is required.