Question

In May 2015, a poll asked a random sample of 1,156 American adults the following question.

"Thinking about how the abortion issue might affect your vote for major offices, would you only vote for a candidate who shares your views on abortion or consider a candidate's position on abortion as just one of many important factors or not see abortion as a major issue?"

It found that 21% of respondents said they will only vote for a candidate with the same views on abortion that they have. Suppose that the sample size had been 4,600 rather than 1,156. Find the margin of error for 95% confidence in this case. (Round your answer to two decimal places?

-------%

Answer 1

Solution

In May 2015, a poll asked a random sample of 1,156 American adults the following question.

"Thinking about how the abortion issue might affect your vote for major offices, would you only vote for a candidate who shares your views on abortion or consider a candidate's position on abortion as just one of many important factors or not see abortion as a major issue

The margin of error for a sample of size 1,156 = z*√p(1-p)/n = 1.96*√0.21(1-0.21)/1156 = 0.02348

The margin of error for a sample of size 4,600 = z*√p(1-p)/n = 1.96*√0.21(1-0.21)/4,600 = 0.01177

The margin of error for a sample of 4,600 is smaller than the margin of error for a sample of 1,156.

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