Question

multiple choice 1 point a cable news show displays the results of a poll for a two - candidate runoff election between candidate a and candidate b. the poll shows that candidate a is leading with 53% of the vote. in small print at the bottom of the graphic, it says ±4.9%. which of these statements is true about this poll? candidate a will win because the mean percentage for the poll is greater than 50%. candidate a cannot get more than 58% of the vote. the poll should not be trusted since it has a margin of error attached to it. the poll predicts that between 48.1% and 57.9% of voters will select candidate a in the election. clear my selection previous submit

Explanation:

Step1: Understand Margin of Error

The poll has a margin of error of ±4.9% and the mean percentage for Candidate A is 53%. To find the range, we calculate the lower and upper bounds.
Lower bound: \( 53 - 4.9 = 48.1 \)
Upper bound: \( 53 + 4.9 = 57.9 \)

Step2: Evaluate Each Statement

• "Candidate A will win because the mean percentage for the poll is greater than 50%": The margin of error means the actual percentage could be as low as 48.1%, so we can't be certain of a win. Eliminate this.
• "Candidate A cannot get more than 58% of the vote": The upper bound is 57.9, which is less than 58, but this is not the main point of the margin of error. Eliminate this.
• "The poll should not be trusted since it has a margin of error attached to it": Margins of error are a standard part of polls to show uncertainty, so the poll can be trusted with this info. Eliminate this.
• "The poll predicts that between 48.1% and 57.9% of voters will select candidate A in the election": This matches the range we calculated (48.1 to 57.9) using the mean (53) and margin of error (±4.9). This is correct.

Answer:

The poll predicts that between 48.1% and 57.9% of voters will select candidate A in the election