Question

A group conducted a poll of 2055 likely voters just prior to an election. The results of the survey indicated that candidate A would receive 45​% of the popular vote and candidate B would receive 43​% of the popular vote. The margin of error was reported to be 2​%. The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means. What does it mean to say the race was too close to​ call? A. The margin of error suggests candidate A may receive between 43​% and 47​% of the popular vote and candidate B may receive between 41​% and 45​% of the popular vote. Because the poll estimates overlap when accounting for margin of​ error, the poll cannot predict the winner. B. Since the difference between the percentages of the popular vote for the candidates is less than the 12​% of voters that are​ undecided, the poll cannot predict the winner. C. Since the poll results do not show that one of the candidates has more than​ 50% of the popular​ vote, the poll cannot predict the winner. D. Since the estimated proportions depend on the level of​ confidence, the candidate predicted to receive the greater percentage of the popular vote changes for different levels of​ confidence, so the poll cannot predict the winner.

Answer 1

Margin of Error = 2%

Confidence interval of percentage of votes to A is,

(45% - 2%,  45% + 2%)

(43%, 47%)

Confidence interval of percentage of votes to B is,

(43% - 2%,  43% + 2%)

(41%, 45%)

Since both intervals overlap, the survey cannot predict a winner. The answer is,

A. The margin of error suggests candidate A may receive between 43​% and 47​% of the popular vote and candidate B may receive between 41​% and 45​% of the popular vote. Because the poll estimates overlap when accounting for margin of​ error, the poll cannot predict the winner.