Question

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 $0.54 \pm 0.06$. what is the correct interpretation of the 95% confidence interval?
we are 95% confident that 54% of all voters would vote for roberts.
there is a 5% chance that less than 48% or more than 60% of voters would vote for roberts.
there is a 95% probability that roberts would receive between 48% and 60% of the votes.
we are 95% confident that the interval from 0.48 to 0.60 captures the true proportion of voters who would vote for roberts.

Explanation:

A 95% confidence interval does not assign probability to the true population proportion or claim the sample proportion is the population value. Instead, it states we are 95% confident the interval contains the true population proportion. The interval here is $0.54 - 0.06 = 0.48$ to $0.54 + 0.06 = 0.60$.

Answer:

We are 95% confident that the interval from 0.48 to 0.60 captures the true proportion of voters who would vote for Roberts.