Statistics?

Question

I am stuck on this problem. I would appreciate your expertise in telling me how to solve it so I know for the next time.

Thanks

Determine the percentage of all samples of 64 public school teachers that have mean salaries within $1000 of the population mean salary of $43,658. Interpret your answer in terms of sampling error.
Repeat this for samples of size 256.

The standard deviation is $8000.

Answer 1

Do you know the standard deviation of the salaries? You need it to be able to answer.

edit: Since you start by taking many samples of size 64 from the population, the average value for these mean salaries would be 43,658 and the standard error would be 8000/sqrt(64) = 1000, which would be treated like it's a standard deviation. So to be within $1000 of the population mean, you would end up being within one standard error of the mean. That would be around 68% according to the empirical rule.

Sampling error is the amount the sample mean is away from the population mean. In this case, the sampling error would be less than $1000 around 68% of the time.

For samples of size 256, the population mean would still be $43,658, but now the standard error would be 8000/sqrt(256) = 500. So if the mean of the salaries was within $1000 of the population mean, then it had to be within two standard errors of the mean. According to the empirical rule, that would be 95%. The sampling error would be less than $1000 95% of the time.

Answer 2

Look in the directions to this problem. Chances are you have a standard deviation which you did not give us here. It is pretty much vital to know that in order to do the problem. Once you know that, you'll most likely use a z-score formula such as
z= 1000/(s/SQR(64)) ... inserting your standard deviation for "s"
You'll most likely use a table to determine the percentage of scores that are between -z and +z for the value you get.