TABLE OF CONTENTS Statistical tests involve testing claims by collecting and analyzing data. There are many problems that are concerned with testing some conjecture or hypothesis. We specify two competing hypotheses. One hypothesis which is called the null hypothesis and denoted by H 0 is the statement that observed results are due to chance. The other hypothesis which is called the alternative hypothesis and denoted by H 1 is the hypothesis we try to establish. We collect data and determine if we should reject H 0 in favor of H 1. The question is whether or not the data are much more consistent with H 1 than H 0 in which case H 0 should be rejected. Statistical hypothesis testing enables us to distinguish chance effects from real ones.
In a jury trial, we would test:
H 0: defendant is not guilty versus H 1: defendant is guilty.
Does the evidence presented to the jury indicate that we should reject H 0 in favor of H 1?
The objective of a test is to determine if the data will discredit the null hypothesis convincingly so as to make the alternative hypothesis seem quite reasonable. If there is some small doubt, then the null hypothesis is not rejected. In the jury trial, one wants to show guilt beyond a reasonable doubt.
The level of significance (or significance level) of a test is the probability of rejecting H 0 when
