Overview of Hypothesis Testing
All facts that are known and accepted are based on empirical evidence. When alternate ideas come to challenge what is previously known, statistics come in handy to determine what hypothesis should be rejected and which one should be accepted.
The null hypothesis, or H0, is the original claim that is being challenged. The alternative hypothesis, HA, is the claim that challenges H0, asserting that the contradictory is true. If the statistical outcome reveals that the null hypothesis is false, we claim to reject H0. If the statistical outcome establishes the sample evidence does not contradict the null hypothesis, we fail to reject H0.
If the wrong decision is made after statistical evaluation, two different types of errors can occur. The first one is made when the null hypothesis is true, yet we reject it. This is called a type 1 error. On the other hand, if we do not reject H0 when it is false, a type 2 error is produced. To further explain these errors, let's take a look at a common example regarding the Judicial System:
H0: The convicted person is innocent.
HA: the convicted person is guilty.
A type 1 error would mean that the person is innocent (H0 is true), yet we are rejecting this claim, thus sending an innocent person to jail.
A type 2 error would mean that the person is not innocent (H0 is false) and we are rejecting it, letting a guilty person go free.
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Source used throughout: Probability and Statistics for Engineering and the Sciences | 9th Edition Jay L. Devore