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January 30, 2015

January 30, 2015

Posted by **Jen** on Monday, June 16, 2014 at 6:50pm.

**Suppose a random sample of size 50 is selected from a population with σ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

Question: The population size is N = 500 (to 2 decimals).

My work:

1.4142 sqrt ( 499/450) = 1.49

I keep getting 1.49 but the computer is marking it wrong. I'm not sure what I am doing incorrectly. Thanks for the help.

- Statistics (Check Answer) -
**MathGuru**, Monday, June 16, 2014 at 7:42pmSome notes on finite population correction factor:

If the population is small and the sample is large (more than 5% of the small population), use the finite population correction factor.

For standard error of the mean, use:

sd/√n

If you need to adjust for the finite population correction factor, use:

sd/√n * √[(N-n)/(N-1)]

N = number in population

n = number in sample

Is the sample size of 50 more than 5% of the population size of 500? Yes, it is, so use the finite population correction factor.

With your data:

10/√50 * √[(500-50)/(500-1)] =

1.4142 * 0.9496 = 1.34

Check these calculations.

I hope this helps.

- Statistics (Check Answer) -
**Jen**, Monday, June 16, 2014 at 8:26pmThank you so much for the help! I completely overlooked using the population correction factor.

- Statistics (Check Answer) -
**MathGuru**, Tuesday, June 17, 2014 at 5:17pmYou are welcome!

I'm glad the explanation helped.

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