Question

A polling agency wanted to test whether a ballot measure would pass with greater than 50% yes votes. The agency sampled 1,000 registered voters selected at random, and 50.6% of the voters favored the ballot measure. The margin of error associated with this poll was ±3%. Based on the poll's results, which of the following statements must be true?

A) The percentage of voters who will vote yes for the ballot measure is 50.6%.
B) The ballot measure will pass with more yes votes than no votes, but the percentage of votes it will receive cannot be predicted.
C) The ballot measure will pass with at least 53.6% of the vote.
D) The poll's results do not provide sufficient evidence to conclude that the ballot measure will pass​

Answer 1

D

Explanation:

The margin of error represents the amount of percentage points that the real value can differ from the value given in the sample. The margin of error is ±3%, meaning that 50.6 (the sample value) ± 3% is the margin of error, resulting in a range of (47.6, 53.6) as our margin of error. Anything in that range can be the true proportion of voters that would vote for the ballot measure. As the range contains value both less than and greater than the 50% needed to pass, it is impossible to say, given the data, that the voters will vote yes or no to the ballot.