The process of hypothesis testing begins with the arrival of a sample statistic
indicating a change may have taken place. Action
may be needed. The sample
may indicate that:
1) The marketing director needs to do something because average sales seem
to be going down.
2) A foreman needs to adjust something because parts may be too heavy and
not pass inspection.
3) Our auditor must test more individual accounts payables to prove the balance
sheet amount is correct..
4) A candidate poll numbers indicate she may be falling behind.
We begin by accepting the conditions of the null
[no change] hypothesis and that the results of our research will seldom
require action. When the test
statistic is extreme enough to happen less than the level of significance, we
accept the alternate, research hypothesis. The marketing director calls a meeting to develop a plan
increase average sales, the foreman makes an adjustment, tests more parts, or shuts down the assembly
line, the auditor samples another batch of payables, and the politician makes more speeches.
What do we do when the sample is not extreme enough to happen less than
or equal to the level of
significance? Some people do not like to say we
accept the null hypothesis because that indicates it is true
and we did not
prove that it was true. Actually, when dealing with probability nothing is really
proven. Indications are it was not false. For this reason, many statistics books
fail to reject the null hypothesis rather than accept the null hypothesis.