#econ #stats 

You can take a sample, and get a sample mean. The sample mean has a distribution of possible answers depending on all the different samples you can take. 
There is also a sample variance, which uses the sample mean and thus has its own distribution and thus its own mean and standard deviation.

standard error: it's the standard deviation of the sample mean.

The mean of the sample means is the same as the mean of the original distribution.

![graphs|200](PXL_20211111_195701910.jpg)
$\bar x$ is an estimate of $\mu_x$.

It's a point estimate.
You use that point estimate plus a margin of error to get a confidence interval. 

On different initial distributions, you have different methods for estimating sample means and variances.

The mean of a sample mean estimator is the mean of the sample. The estimator of the variance is $\frac{\sigma^2}{n}$ where n is the number of samples, and you use the two to make a confidence interval. If you don't know $\sigma^2$ of the population, you have to estimate that as well, and it just means that you need to use the T table and not the normal distribution table. ^ae395f