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Question 450:



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  1. We're given a Margin of Error of +/- $200 and we need to work backwards to arrive at the sample size.
  2. The Margin of Error is made up of the Standard Error of the Mean times a critical value for the confidence level. In this case we're given a 95% Confidence Level. When we lookup .95 using the percentile to z-score calculator we get the z-critical value of 1.96
  3. The standard error of the mean is made up of the standard deviation divided by the square root of the sample size. We know the standard deviation is $1050. 
  4. We setup an equation and solve for the unknown sample size:
    1. ( 1050/SQRT(n) ) *1.96 = 200
    2.  1050/SQRT(n) = 102.04
    3. 1050 = SQRT(n)*102.04
    4. 10.29 = SQRT(n)
    5. 105.88= n

So we'd need to plan on a sample size of 106 fire-fighters to achieve a margin of error of +/- $200 with 95% confidence.

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