A hypothesis is an opinion or claim that can be tested.

In statistics, we validate a hypothesis by finding a low probability of it ** not happening**.

If we can prove it is unlikely that something does __not__ happen, then we can infer that it is likely to happen.

## Null & Alternative Hypotheses

For this reason, we have two hypotheses:

A **null hypothesis**, that something does __not happen__. **(no change =)**

And an **alternative hypothesis**, that something happens **(change <, >, ≠).**

**H(null): **** = the same (null is dull, boring, the same, no change)**

**H(alternative): **** <, >, ≠, (alternative is not the same - think exciting, different, change)**

The alternative hypothesis can be directional** ****one-tailed**: either greater than, **> right-tailed**, or less than, **< left-tailed**.

**You can remember right or left tailed based on which direction the sign is pointing.*

Or, the alternative hypothesis it can be non-directional aka **two-tailed,**** **meaning **not equal to ≠**.

**For example, we may claim that a person is guilty of a crime.**

They are considered innocent until proven guilty.

Our **null hypothesis **is that they are ** not guilty** (innocent).

Our **alternative hypothesis** is that they are **guilty**.

We must have enough evidence, beyond (or greater than >) a reasonable double, before concluding that they are guilty.

Therefore, this would be an example of a r**ight-tailed hypotheses.**

**H (null): Not Guilty (Innocent - no change) = **

**H (alternative): Guilty - change >**

If the jury finds enough aka **significant **evidence extending beyond a reasonable doubt (beyond the blue, into the red zone), they will conclude that the person is guilty (**reject the null hypothesis that they are innocent**).

If the jury does not find enough (**not significant**) evidence, they will conclude the person is not guilty (**do not reject the null**)

More examples of of hypothesis testing, and information about Type 1 and Type 2 Error to come soon!

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