What sample size is necessary for 95% CI?A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions.a. What sample size is necessary if the 95% CI for p is to have a width of at most 0.10 irrespective of p?b. If the legislator has strong reason to believe that at least 23 of the electorate know of her position, how large a sample size would you recommend?

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Skyler Guzman · Accepted Answer

If you want a 95% CI, then it seems to me you need to use k=zα2=1.96, where k is my abbreviation. Also, in your first computation, I think you mean to set w=.1 (not p=.1, because you assume p=12.) And I am puzzled why you set n=10, when n is what you&#039;re trying to find. Finally, I think 0.25 in your equation is p(1−p)=pq=(12)(12)=0.25. With all of that, I do get the same result that you report from the following computation in R.k=1.96;p=.5;q=.5;w=.1k22−k2⋅w2+k4⋅(p⋅q−w2)+w2⋅k4w2The rationale for taking p=q=12 when p is unknown is that this maximizes the required n and thus insures it is large enough for other possible values of p.However, I do not get n=339 when I change the problem so that p=23 and q=13. (I&#039;m not sure whether this is the change you made, but it seems reasonable to me.) This should take care of situations where the true p is 2/3 or greater. Here is what I did get:k=1.96;p=23;q=13;w=.1k22−k2⋅w2+k4⋅(p⋅q−w2)+w2⋅k4w2Because you have what I take to be several typos in your Question, I don&#039;t know where to go from here to help you resolve the discrepancy. Please proofread everything (your Question and my Answer), and make any edits, suggestions, or explanations that might help make the next attempt to help more successful.

What sample size is necessary for 95% CI? A

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