How do you do exactly a sample size calculation for a normal distributed population with known standard deviation, to have a chance of type 2 error of at most 5%. .
Zero hypothesis is:
$$ \mu_0 = 20, \sigma = 1$$
Actual mean of the population is known by the researcher:
$$ \mu = 19.5 $$
With the same standard deviation.
Type II error is not-rejecting a false zero hypothesis.
If the chance of a type II error is at most 5%, what is the minimal sample size you have to have for a alpha of 5%?
I would say it is the calculation of:
$$ P(a<Z<b)$$
Where
$$ Z = \frac{\bar x - \mu}{\sigma/\sqrt(n)} $$
I don't know how to progress. Could someone show how it goes?
