What is the probability that we incorrectly reject
the null hypothesis
when it is actually true?
The probability of such an error is called
the probability of type I error
and is exactly the significance level
But how about the probability that
we incorrectly accept the null hypothesis
when it is actually false?
the probability of type II error
Given the current estimate
of population mean
of standard deviation,
it is possible to find
is known as
of the test,
indicating how correctly
can be accepted when it is actually
true in the following hypothesis test problem
The power of the test can be calculated
with a specific choice of the sample size
The power of the test increases as the sample size increases.
Therefore, we can achieve the desired power of the test
instead by increasing a sample size .
having prescribed the power and the sample size ,
it is possible to derive the
corresponding value .