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Hypothesis testing

When we are conducting hypothesis testing, there will be four possible outcomes can occur:

i.               We accept Ho, and Ho is in fact TRUE
ii.              We accept Ho, and Ha is in fact TRUE
iii.            We reject Ho, and Ho is in fact TRUE
iv.             We reject Ho, and Ha is in fact TRUE

In practice, it is impossible to prove the Ho (null hypothesis) is TRUE. Therefore, if we ACCEPT Ho, then we have actually FAILED to reject Ho!

 If Ho is TRUE and Ho is accepted, or if Ha is TRUE and Ho is rejected, then the correct decision has been made. Therefore, if we accidently rejecting Ho when Ho is actually TRUE, or if Ha is TRUE but now Ho is accepted, then an ERROR has been made. So now the two concepts of ERROR will then be introduced and need to be treated differently.
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