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    Sample size and finite population correction factor

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    The house of representatives has a very controversial bill that will be going to vote. To help formulate his strategy on how to get the bill passed, the chairman of the committee that has been studying the bill wishes to know if there is a division between Democrats and Republicans on the issue or if there is some other basis for the split. To estimate the proportion of Republicans in favor of the bill, how large must a sample of representatives be to estimate the percentage within 3 percentage points with 90% certainty. Assume there are 538 representatives. Use the finite population correction factor and develop your own formula for computing the answer.

    Please show all formulas.
    Answer should be n<= 314.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf
    https://brainmass.com/statistics/sample-size-determination/sample-size-finite-population-correction-factor-29101

    SOLUTION This solution is FREE courtesy of BrainMass!

    See the attached file.
    sp=standard error of proportion=square root of (pq/n) square root of ((N-n)/(N-1))
    where square root of ((N-n)/(N-1)) is the finite population multiplier
    where N is the population size and n is the sample size

    confidence interval= 90%
    We have to find z corresponding to 5% in each of the two tails. (100%-2x 5%=90%)
    Z corresponding to 90% and two tailed test is 1.6449

    We have to see that Z* sp < 3%
    or sp < 3%/Z
    or sp < 0.018238 =3%/1.6449
    But
    sp=standard error of proportion=square root of (pq/n) square root of ((N-n)/(N-1))

    The maximum value of standard error of proportion for any given value of n is when p=q=0.5
    pq= 0.25 =0.5*0.5
    square root of ((N-n)/(N-1))= square root of ((538-n)/(538-1))=square root of (538-n)/537)
    as N= 538

    Thus
    square root of (pq/n) square root of ((N-n)/(N-1))< 0.018238
    Or square root of (0.25/n) square root of ((538-n)/(537))< 0.018238

    Or squaring both sides

    (0.25/n) (538-n)/(537)< 0.00033262

    Or (538-n)/n= 0.714468

    Or 538/n -1 = 0.714468

    or 538/n= 1.714468
    or n= 313.8 which when rounded off into a whole number= 314

    Answer: sample size = 314.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf>
    https://brainmass.com/statistics/sample-size-determination/sample-size-finite-population-correction-factor-29101

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