## sample mean, population mean, pop. st. dev. 5000, sample of

Standard deviation, mean, variance, z-scores, t-tests, etc.
yabo2k
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Joined: Tue Apr 28, 2009 9:09 pm
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### sample mean, population mean, pop. st. dev. 5000, sample of

the average annual salary for government employee is 41979. Use this figure as the population mean and assume that the population std dev is 5000. suppose that a random sample of 50 employees will be selected from the population.

1) calculate the value of the standard error of the mean? i got 707.1
2) what is the probability that the sample mean will be laess thatn 41979? explain. (can't figure this out)
3) what is the probability the sample mean will be within 1000 of the population mean? i got .8414

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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a) The standard error of the sample mean is the population deviation, divided by the square root of the sample size, so:

. . . . .$\frac{5000}{\sqrt{50}}\, \approx\, 707.1067812$

b) Since the value they use is the mean value, there isn't any calculating to do here. Just use the meaning of what the population mean is. By definition, what is the probability that a given value will be below this mean value?

c) I don't know what software you have, or if you're working from tables. You can either plug-n-chug, or use the z-scores, either doing both parts at once, or else P(X < 42979) - P(X < 40979). Either way, I get about the same answer you do. (If you're working from tables, there can be round-off error. But you're certainly in the ballpark!)