Question

What is the standard error of a sampling distribution when σ (sigma) = 24 and n = 144? (Points : 2)
20
.167
2.0
unable to determine

Answer 1

Try this:\[\frac{ \sigma }{ \sqrt{n} }\]

Answer 2

I would say unable to determine is more accurate. The standard error is a statistic and is a function of your sample data. Thus, it uses an estimated variance, so standard error = \(\sqrt{s^2}\) The standard deviation uses the square root of the POPULATION variance, which is what is given here, which is \(\sqrt{\sigma^2}\).

Answer 3

@kirbykirby : Thank you for your thoughtful input. I've looked up "standard error of a sampling distribution and have come up with the following resource:

http://vassarstats.net/dist.html

Its definition of "standard error" differs from yours. Would you please go there and determine whether or not you'll stick by your definition or the one in this online doc?

I tried doing the calculation according to my interpretation of "standard error," and found that my result matches one of the several possible answers given.

Thanks for your efforts.

Answer 4

@cbkb1234 : Please get involved in this discussion yourself. Thanks.

Answer 5

Ok I did more research on this. Apparently the definition of standard error varies slightly from person-to-person/institution-to-institution. At my university, we use the following distinction for standard error and standard deviation (of the population and sample mean) http://en.wikipedia.org/wiki/Standard_error (which is what I outlined).

Some people though apparently use standard deviation to refer when using random variables, and standard error when using realizations of the random variables.

Some use your definition above for the standard error, and the standard deviation is is sigma itself.

Some just use the terms interchangeably.

Answer 6

@mathmale

Answer 7

Thanks very much for your research and input. I appreciate it. Always learning something new at this end. Best to you!

Answer 8

I appreciate learning these differences too. It would be more helpful if they standardized the definition for these terms (no pun intended).