n = ,
it is assumed that the test statistic
has the t-distribution with df = n-1 degrees of freedom with true population mean . If the true standard deviation is known, use df = +Inf (the infinity ).
We can calculate the critical region corresponding to the level . Or, the numerical values of critical region can be found in t-distribution Table.
The appropriateness of this calculation can be ensured if (a) the sample distribution is approximately normal (the use of QQ plot is recommended), or (b) the sample size is adequately large (as a rule of thumb it is desirable to have ).
Conversely when the test statistic T is given, we can find the corresponding so that the value T belongs to the critical region, and call it p-value.
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