Question

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?

Answer 1

The sample proportion minus the margin of error is greater than 0.05, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.

Explanation:

Sample proportion is 55%

margin of error is E = 3%

Confidence interval = (p-E) to (p+E)

= (55-3) to (55+3)

= 52% to 58%

Lower limit is above 50%, which means that the candidate Taylor has majority of votes in his favor.

Answer 2

It's not possible to reach a conclusion about who will vote candidate Taylor because this is a random sample and not a population census or experiment.

Explanation:

It is impossible to reach a conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city.