Final answer:
To construct a 90% confidence interval with a margin of error no larger than 0.05, the pollster would need to sample at least 272 voters, using the standard formula for sample size estimation in proportions with p = 0.5 and a z-score of 1.645.
Step-by-step explanation:
To find the sample size needed for the pollster to construct a 90% confidence interval for the proportion who support the incumbent candidate for mayor with a maximum margin of error of 0.05, we can use the formula for the sample size of a proportion:
n = (Z^2 * p * (1-p)) / E^2
where Z is the z-score for the desired confidence level, p is the estimated proportion (we use 0.5 if we lack prior information, since it maximizes the sample size), and E is the desired margin of error.
Since we don't have specific information about the proportion who support the incumbent, we use p = 0.5. For a 90% confidence interval, the z-score is approximately 1.645. Plugging these values into the formula, we get:
n = (1.645^2 * 0.5 * 0.5) / 0.05^2 = 271.04
Therefore, the pollster would need to sample at least 272 voters to achieve the desired margin of error.