A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. What is the correct interpretation of the 95% confidence interval?

The interval is 0.54 ± 0.06, so its endpoints are 0.48 and 0.60. A 95% confidence level means that the method used to make intervals would capture the true population proportion in about 95% of repeated random samples. Thus, we are 95% confident that the interval from 0.48 to 0.60 captures the true proportion of voters who would vote for Roberts; it does not mean the fixed population proportion has a 95% probability of lying in this particular interval.

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