> For the complete documentation index, see [llms.txt](https://stephanosterburg.gitbook.io/scrapbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://stephanosterburg.gitbook.io/scrapbook/math/statistics-and-probability/significance-tests-hypothesis-testing.md).

# Significance Tests (hypothesis testing)

### Example

Four siblings random lottery who cleans:

* Assume truly random
* P(Bill not picked on a night) = 3/4
* P(Bill not picked 3 nights in a row) = 3/4 \* 3/4 \* 3/4 = 27/64 = 0.42 = 42%
* 12 nights in a row => (3/4)^12 = 0.032 or 3.2%

## Idea behind hypothesis testing

![](https://3501392451-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LLZ89zzVxrdnG1RG6CA%2F-LhXgPmBwJHHxXYTNgND%2F-LhXjPesPH8HGHubLBl6%2FScreen%20Shot%202019-06-16%20at%205.01.44%20PM.png?alt=media\&token=6fdeb68a-36e1-407c-a36c-ae1fb2564e8c)