Question

when testing a new hypothesis against its alternative hypothesis, your decision is to either reject the null hypothesis or fail to reject the null hypothesis . Why don’t we claim to accept the null hypothesis? Give an analogy for this concept.

Answer 1

In hypothesis testing, we test the evidence against the null hypothesis. The null hypothesis assumes that whatever we are trying to prove did not happen.

EXAMPLE:

Suppose we want to test whether two teaching methods result in diffrent performance in examination.

H0: Null hypothesis: 1 = 2 (Same performance)

HA: Alternative hypothesis: 1 2 ( Different performance)

In hypothesis testing, we test the evidence against null hypothesis.

In this case, we test whether there are evidences for the two teaching methods result in different performance in examination.

In case we get such evidence of two teaching methods result in different performance, we reject the null hypothesis.

In case we do not get such evidence, we fail to reject the null hypothesis.

Thus, the hypothesis test has only two possible outcomes:

Outcome 1: Reject the null hypothsis: p value . We conclude that the alternative hypothesis is true at (1-) % confidence level.

Outcome 2: Fail to reject the null hypothesis: p value > . We conclude that there is not enough evidence is available to suggest the null hypothesis is false at (1 - ) % confidence level.