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Consider a two-way election race between Ahmed and Amara to elect a new student council president at a Carleton University. Suppose that 500 students were randomly selected from the population of students. Among them, $237$ students said that they would vote for Ahmed. (a) Give a point estimate of the proportion of all students who will vote for Ahmed. (b) Estimate the proportion of all students who will vote for Ahmed with $97\%$ confidence.

My work:

I first found the mean: $237/500 = 0.474,$ and I know that the sample size is 500, but I'm not sure how to go about finding the confidence interval without the variance.

Any help is greatly appreciated!

EDIT:

While trying some more I got $0.474 + 2.96*\sqrt{0.474*0.526)/500},$ which equals $[0.4079,0.5401]$, but the answer says that the interval is $[0.426,0.522].$ Still not sure where I am going wrong!

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  • $\begingroup$ I put some TeX symbols into your question to make it easier to read. Glad you found your way to the right answer. Maybe select 'edit' to have a look at the edits for future reference. $\endgroup$ – BruceET Dec 19 '15 at 3:30
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Found out where I was going wrong after my EDIT, used the wrong critical value for a 97% confidence interval, should have been 2.170, which results in the correct confidence interval.

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