Model and hypotheses

In both examples in the first page of this section, there was knowledge of the population standard deviation σ (at least when H0 was true). This greatly simplifies the problem of finding a p-value for the test.

In the following examples, the population standard deviation, σ, can be treated as a known value.

In both examples, the hypotheses were of the form,

H0 :   μ  =  μ0
HA :   μ  ≠  μ0

Summary Statistic and p-value

We now explain how the p-value for testing a population mean can be obtained when σ is a known value.