Here we are interested in the plausibility of the hypothesis
regarding the ``true'' population mean . is called an alternative hypothesis, and together with null hypothesis it forms the basis of hypothesis testing. becomes the opposite of , and is used in the context of determining whether we can reject `` in favor of .''
The significance level has to be chosen from or ( is not common in this particular test). Under the null hypothesis , it is ``unlikely'' that the t-statistic lies in the critical region specified in the table below. If so, it suggests significant evidence against the null hypothesis .
|Hypotheses||Critical region to reject|
Alternatively, the p-value can be calculated so that ``p-value '' is equivalent to the t-statistic being observed in the critical region. When the null hypothesis is rejected (i.e., p-value ), it is reasonable to calculate the confidence interval estimating the population mean .