#### Hypothesis Test

Testing hypotheses is a common part of statistical inference. To formulate a test, the question of interest is simplified into two competing hypotheses, between which we have a choice. The first is the null hypothesis, denoted by H0, against the alternative hypothesis, denoted by H1 . For example with 50 years of annual rainfall totals a hypothesis test could be whether the mean is different in El Nino and Ordinary years. Then usually • The null hypothesis, H0, is that the two means are equal, i.e. there is no difference. • The alternative hypothesis, H1, is that the two means are unequal, i.e. there is a difference. If the 50 years were considered as being of three types, El Nino, Ordinary, La Nina then usually: • The null hypothesis, H0, is that all three means are equal. • The alternative hypothesis, H1, is that there is a difference somewhere between the means. The hypotheses are often statements about population parameters. In the first example above it might be: • H0, is that µE = µO. • H1, is that µE ≠ µO. The outcome of a hypothesis test is either • Reject H0 in favour of H1, or • Do not reject H0.