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Homework Help: 95% CI for the population proportion

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data

    A 95% CI for the population proportion of professional tennis players who earn more than $2 millions a year is found to be [0.82, 0.88]. Given this information the sample size that was used was approximately A) 545 B) 382 C) 233 D) 378
    Answer: A) 545


    2. Relevant equations

    Z = 1.96 for 95% CI
    +/- Z[S/sqrt(n)] = 0.03


    3. The attempt at a solution
    +/- 1.96 [0.03)/sqrt(n) = 0.03
    sqrt(n) = 1.96(2)/0.03
    sqrt(n) = 130
    n = 11.4 <-- this incorrect.

    The answer should be A) 545. But where did i go wrong? How do i solve this problem? Thanks.
     
  2. jcsd
  3. Feb 14, 2010 #2
    first use the fact that .03 = 2 *(1.96)*sqrt(p(1-p)/n) now solve for n and plug in the two bounds for the CI given. you will find that n lies between 450 and 630 hence the answer.
     
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