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#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.
\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