Question

If you drew a random sample of size 40 from a population of students having a mean (μ) Math Achievement Test score of 200 and a standard deviation (σ) of 20

1.What would be the average of all the sample Math Aptitude means you could have obtained for samples of size 40? Mx= ?

2.Not all your possible sample averages would have been the same. What would be their “standard” distance from the population average of 200? σx= ?

3.If you had sampled an n=100 instead of 40, what would be the standard difference from 200 now?

Answer 1

Result:

If you drew a random sample of size 40 from a population of students having a mean (μ) Math Achievement Test score of 200 and a standard deviation (σ) of 20

1.What would be the average of all the sample Math Aptitude means you could have obtained for samples of size 40?

Mx= 200

2.Not all your possible sample averages would have been the same. What would be their “standard” distance from the population average of 200?

σx= σ /sqrt( n) = 20/sqrt(40)

=3.16228

3.If you had sampled an n=100 instead of 40, what would be the standard difference from 200 now?

σx= σ /sqrt( n) = 20/sqrt(100)

=2