# Thread: Margin of Error and Estimating Population Mean

1. ## Margin of Error and Estimating Population Mean

I'm working on a study assignment and I'm totally stuck on these two subquestion of the main set:

* In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was deteremined. Assume a population standard deviation of 450-kw hours.

-At 95% confidence, the size of the margin of error is?

-If the sample mean is 1,858KWH, the 95% confidence interval estimate of the population mean is?

I've been looking all over wikipedia and google at explanations of these topics but I'm pretty much lost on the concepts. Could someone help run me through what formula(s) to use and maybe how to go about it (ie. what variables signify what values)?

Thank you guys!

2. Originally Posted by chbrules
I'm working on a study assignment and I'm totally stuck on these two subquestion of the main set:

* In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was deteremined. Assume a population standard deviation of 450-kw hours.

-At 95% confidence, the size of the margin of error is?

-If the sample mean is 1,858KWH, the 95% confidence interval estimate of the population mean is?

I've been looking all over wikipedia and google at explanations of these topics but I'm pretty much lost on the concepts. Could someone help run me through what formula(s) to use and maybe how to go about it (ie. what variables signify what values)?

Thank you guys!
If the population SD is $\sigma$ then the SE of the mean of a sample of size $N$ is $\sigma/\sqrt{N}$.

Then assuming that the CLT applies (that is we can assume the distribution of sample means is normal with SD equal to the SE) the 95% interval is $1.96 \times \sigma /\sqrt{N}$

CB