> For the complete documentation index, see [llms.txt](https://jamesbrayy.gitbook.io/atar/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jamesbrayy.gitbook.io/atar/specialist/sample-means.md).

# sample means

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## **relevant calcs**

* $$\sigma\_s = \frac{\sigma\_p}{\sqrt{n}}$$
* $$\mathrm{m.e.}\_s = k , \sigma\_s$$
* $$X \sim N(\mu, \sigma^2)$$

## **central limit theorem**

* the central limit theorem states that the distribution of the sample means converges to a standard normal distribution for large sample numbers
* if a population parameter is normally distributed, than the central limit theorem can be applied even if $$n < 30$$

## **confidence intervals**

* the \_\_% confidence interval calculated means that \_\_% of all confidence intervals calculated will contain the true mean of the population
* if confidence intervals overlap between a statement and the measurement then there is evidence to suggest that at the \_\_% level the statement is true
* a 100% confidence interval is not generally possible as a 100% confidence interval implies finite boundaries while a normal distribution is unbounded