## Question 450:

1## Answer:

No answer provided yet.- We're given a Margin of Error of +/- $200 and we need to work backwards to arrive at the sample size.
- 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
- 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.
- We setup an equation and solve for the unknown sample size:
- ( 1050/SQRT(n) ) *1.96 = 200
- 1050/SQRT(n) = 102.04
- 1050 = SQRT(n)*102.04
- 10.29 = SQRT(n)
- 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.