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A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was 24%. The margin of error for the survey was 5%. Which of the following is a reasonable value for the actual percentage of the population that prefers Candidate A?

Question

A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was 24%. The margin of error for the survey was 5%. Which of the following is a reasonable value for the actual percentage of the population that prefers Candidate A?

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Solution

The margin of error in a survey is a measure of the range within which the true value (in this case, the true percentage of voters who prefer Candidate A) is likely to fall.

Given that the survey found that 24% of respondents prefer Candidate A, and the margin of error is 5%, this means that the actual percentage of the population that prefers Candidate A could reasonably be as low as 19% (24% - 5%) or as high as 29% (24% + 5%).

So, any value within this range (19% to 29%) would be a reasonable value for the actual percentage of the population that prefers Candidate A.

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