Results 1 to 3 of 3

Math Help - [SOLVED] population proportion

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    206

    [SOLVED] population proportion

    2 populations are independently surveyed using s.r.s of size n, and 2 proportions, p1 and p2, are estimated. It is expected that both population proportions are close to 0.5. What should the sample size be so that the standard error of the difference, \hat p_1-\hat p_2 will be less than 0.02?

    I can find \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}(\frac{N-n}{N-1})} for the individual component, but I don't know how to apply for \hat p_1-\hat p_2.
    Answer is 1250.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I would set

    \sigma_{\hat p_1-\hat p_2}=\sqrt{ {p_1(1-p_1)\over n_1 }+{p_2(1-p_2)\over n_2 } }\le .02

    Then let all the p's equal .5 and n_1=n_2=n

    This leads to

    \biggl({1\over .02}\biggr)^2\le 2n

    I also get 1250 or LARGER for BOTH of the n's.
    Last edited by matheagle; August 30th 2009 at 08:05 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    you had the st deviation for a hypergeometric, but for only ONE parameter.

    So n_1\ge 1250 and n_2\ge 1250
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Point estimate for the true population proportion
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 15th 2009, 09:54 AM
  2. population proportion
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 4th 2009, 12:43 AM
  3. hypothesis test for a population proportion
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 1st 2009, 09:03 PM
  4. population proportion
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 29th 2007, 10:48 AM
  5. population proportion
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 4th 2007, 03:28 AM

Search Tags


/mathhelpforum @mathhelpforum