Question

In May 2015, a poll asked a random sample of 1,089 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. What is the approximate margin of error for 95% confidence? (Round your answer to two decimal places.)

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Answer 1

Answer : In May 2015, a poll asked a random sample of 1,089 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.

Solution :

Given, sample size, n = 1089,

sample proportion, p̂ = 21% = 0.21.

At, 95% confidence, α = 0.05

Hence, the critical value = Z_{α/2} = Z_{0.025} = 1.96.

Hence,

margin of error = Z(α/2)*√{p̂(1-p̂) / n}

                            = 1.96 * √{0.21(1 - 0.21)/1089}

                           =1.96 * √0.00015

                           = 1.96 * 0.01225

                           = 0.02401

                           = 2.40%

Therefore, the approximate margin of error for 95% confidence is 2.40 %.