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We estimate the standard deviation of the population:
and we get the standard deviation of the mean:
now we can compute the tvalue:
for the non directed Hypothesis we have a critical tvalue of for the directed Hypothesis we have a critical tvalue of
The obtained tvalue is greater that the critical tvalue. The grade point average of the 22 pupils is different from the populations’ GPA.
BrightStat Output of this example
This is a fictitious example. 
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