Question

A newspaper poll found that 54% of the respondents in a random sample of voters from a district in a city plan to vote

for candidate Roberts rather than the candidate running against him. A 95% confidence interval for the population
proportion was 0.54 0.06. What is the correct interpretation of the 95% confidence interval?
O We can be 95% confident that 54% of all voters will vote for Roberts.
There is a 95% probability that Roberts will receive between 48% and 60% of the votes.
There is a 5% chance that less than 48% or more than 60% of voters will vote for Roberts.
We can be 95% confident that the true proportion of voters who will vote for Roberts is between 48% and 60%.
If we repeatedly took samples of the same size from voters from this city, approximately 95% of those samples
would have between 48% and 60% of the sample voting for Roberts.

Answer 1

The correct interpretation of the 95% confidence interval is that we can be 95% confident that the true proportion of voters who will vote for candidate Roberts is between 48% and 60%.

Step-by-step explanation:

The correct interpretation of the 95% confidence interval is:

1. We can be 95% confident that the true proportion of voters who will vote for candidate Roberts is between 48% and 60%. This means that if we were to repeat the sampling process, approximately 95% of those samples would have between 48% and 60% of the voters voting for candidate Roberts.

Answer 2

We can be 95% confident that the true proportion of voters who will vote for Roberts is between 48% and 60%.