A poll was conducted two weeks before an election and showed that the incumbent would win with 56% of the vote and a margin of error of 4%.

If the incumbent needs to receive at least half the votes to win the election, can there be confidence in the incumbent’s victory?

A. Yes, because the lowest the incumbent could receive is 52% of the vote.
B. Yes, because the poll stated that the incumbent will win with 60% of the vote.
C. No, because she could receive as low as 4% of the vote.
D. None of the above

Yes, there can be confidence in the incumbent's victory based on the poll, as the lowest they could receive considering the margin of error is 52%, which is still over the 50% threshold needed to win the election. Therefore, The correct option is a. Yes, because the lowest the incumbent could receive is 52% of the vote.

Explanation:

When evaluating the confidence in an incumbent's victory based on poll data, it is essential to consider the stated percentage of the vote they are expected to receive and the margin of error. The poll predicts that the incumbent will win with 56% of the vote with a margin of error of "+/- 4%". Considering the margin of error, the lowest percentage of the vote that the incumbent could receive is 52% (56% - 4%), which is still above the required 50% threshold needed to win the election. Hence, the most accurate answer to the student's question would be "Yes, because the lowest the incumbent could receive is 52% of the vote", which corresponds to option a. This assumes no other factors come into play and that the poll is representative of the actual population.