failing to reject the null hypothesis when it is false.

the probability of Y falling in the critical region when the null hypothesis is true is ALPHA II.

failing to reject the null hypothesis when it is true.

How do you know which hypothesis to put in H0 and which one to put in Ha? Typically, the null hypothesis says that nothing new is happening; the previous result is the same now as it was before, or the groups have the same average (their difference is equal to zero). In general, you assume that people’s claims are true until proven otherwise. So the question becomes: Can you prove otherwise? In other words, can you show sufficient evidence to reject H0?

rejecting the null hypothesis when it is true.

rejecting the null hypothesis when it is false.

Definition: Assuming that the null hypothesis is true, the p value isthe probability of obtaining a sample mean as extreme or more extreme than thesample mean actually obtained.

rejecting the null hypothesis when the alternative is true.

Before actually conducting a hypothesis test, you have to put two possible hypotheses on the table — the null hypothesis is one of them. But, if the null hypothesis is rejected (that is, there was sufficient evidence against it), what’s your alternative going to be? Actually, three possibilities exist for the second (or alternative) hypothesis, denoted Ha. Here they are, along with their shorthand notations in the context of the pie example:

not rejecting the null hypothesis when the alternative is true.