Here we are interested in the plausibility of the hypothesis
regarding the ``true'' population mean . is called an alternative hypothesis, and together with the null value it forms the basis of hypothesis testing. The null hypothesis is used in the context of determining whether we can reject `` in favor of .''
The test procedure, known as t-test, is based upon the sample mean and the sample standard deviation from a data set of size . Then the discrepancy between the sample mean and the ``assumed'' null value of population mean is measured by the test statistic
The significance level has to be chosen from 0.01 or 0.05 ( 0.1 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 in favor of .
|Alternative hypothesis||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 .