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Inference from sample statistics and margin of error SAT question

Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.

Poll Results

Angel Cruz
Terry Smith

The table shows the results of a poll. A total of voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if people vote in the election, by how many votes would Angel Cruz be expected to win?

ExplanationShow

Choice B is correct. It's given that out of voters responded that they would vote for Angel Cruz. Therefore, the proportion of voters from the poll who responded they would vote for Angel Cruz is . It’s also given that there are a total of voters in the election. Therefore, the total number of people who would be expected to vote for Angel Cruz is , or . Since of the total voters would be expected to vote for Angel Cruz, it follows that , or voters would be expected not to vote for Angel Cruz. The difference in the number of votes for and against Angel Cruz is , or votes. Therefore, if people vote in the election, Angel Cruz would be expected to win by votes.

Choice A is incorrect. This is the difference in the number of voters from the poll who responded that they would vote for and against Angel Cruz.

Choice C is incorrect. This is the total number of people who would be expected to vote for Angel Cruz.

Choice D is incorrect. This is the difference between the total number of people who vote in the election and the number of voters from the poll.

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