A systematic way to make a decision of whether to reject or not reject the null hypothesis
is to compare the p-value and a preconceived αα (also called a "significance level").
A preconceived αα is the probability of a Type I error (rejecting the null hypothesis when
the null hypothesis is true). It may or may not be given to you at the beginning of the
problem.
When you make a decision to reject or not reject HoHo, do as follows:
- If α>p-valueα>p-value, reject HoHo. The results of the sample data are significant. There is
sufficient evidence to conclude that HoHo is an incorrect belief and that the alternative
hypothesis, HaHa, may be correct.
- If αα<p-valuep-value, do not reject HoHo. The results of the sample data are not significant.
There is not sufficient evidence to conclude that the alternative hypothesis, HaHa, may
be correct.
- When you "do not reject HoHo", it does not mean that you should believe that HoHo is true. It
simply means that the sample data has failed to provide sufficient evidence to cast serious
doubt about the truthfulness of HoHo.
Conclusion: After you make your decision, write a thoughtful conclusion about the
hypotheses in terms of the given problem.
- Hypergeometric Probability:
A discrete random variable (RV) with characteristics:
- There is a fixed number of trials.
- The probability of success is not the same from trial to trial, so it is not Bernoulli trials.
The typical example is sampling from a mixture of two groups of items, when we are interested in the only one.
XX is defined as the number of successes out of the total number chosen. The notation is:
X~H(r,b,n).X~H(r,b,n). size 12{X "~" H \( r,b,n \)} {}, where
rr = number of items in the group of interest,
bb = number of items in the group not of interest, and
nn = number of items chosen.
- p-value:
The probability that event will happen purely by chance assuming the null hypothesis is true. The smaller p-value, the stronger the evidence is against the null hypothesis.
