Hypothesis testing addresses the important question of how to choose among alternative propositions while controlling and minimizing the risk of wrong decisions. A hypothesis that is tested for possible rejection is called null hypothesis H0 and the hypothesis which is opposite to this is the alternative hypothesis H1. There are two basic types of decision problems that can be considered in a hypothesis testing procedure.
(a) whether a population parameter has changed from or differs from a particular value.
(b) whether the sample has come from the population that has a parameter value less than or more than the hypothesized value.
The set of all possible values of the sample statistic is referred to as the sample space. The test procedure divides the sample space into two parts called the acceptance region and the rejection region (critical region). In the case of the two-tailed test, we find two values C1 and C2 which set the limits on the amount of sampling variation consistent with the null hypothesis H0. For the one-tailed test, we find only one value C1
When hypothesis H0 is rejected when it is true the error is Type I error. When H0 is accepted when it is false it is called Type II error. When the calculated value of the test statistic is less than the table value, we accept the null hypothesis H0 ; otherwise, accept alternative hypothesis H1.
