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# Hypothesis Testing

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 right-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!