Question

a researcher for a polling organization used a random sample of 1,540 residents in a city to construct a 95 percent confidence interval for the proportion of voters who would vote for candidate jones. the resulting confidence interval was $0.480 \pm 0.025$. what is the correct interpretation of the confidence interval?
a proportion of 0.455 and 0.505 of respondents think that jones has a 95% chance to win.
if 95% of all the voters voted, then jones would receive between 45.5% and 50.5% of the votes.
the polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for jones.
if we repeatedly sampled voters from this city, taking samples of size 1,540, approximately 95% of those samples would have between 45.5% and 50.5% voting for jones.

Explanation:

A 95% confidence interval for a population proportion means we are 95% confident that the interval contains the true proportion of all city voters who would vote for Jones. First, calculate the interval bounds: $0.480 - 0.025 = 0.455$ and $0.480 + 0.025 = 0.505$. The correct interpretation focuses on capturing the true population proportion, not sample proportions, vote outcomes, or win probabilities.

Answer:

C. The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.