In May 2015, a poll asked a ra
In May 2015, a poll asked a random sample of 1,089 Americanadults the following question.
“Thinking about how the abortion issue might affect your votefor major offices, would you only vote for a candidate who sharesyour views on abortion or consider a candidate’s position onabortion as just one of many important factors or not see abortionas a major issue?”
It found that 21% of respondents said they will only vote for acandidate with the same views on abortion that they have. What isthe approximate margin of error for 95% confidence? (Round youranswer to two decimal places.)
——–%
Answer:
Answer : In May 2015, a poll asked a random sample of 1,089American adults the following question. “Thinking about how theabortion issue might affect your vote for major offices, would youonly vote for a candidate who shares your views on abortion orconsider a candidate’s position on abortion as just one of manyimportant factors or not see abortion as a major issue?”
It found that 21% of respondents said they will only vote for acandidate 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 is2.40 %.
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