This section explains how to compute a significance test for the mean of a normally-distributed variable for which the population standard deviation (σ) is known. In practice, the standard deviation is rarely known. However, learning how to compute a significance test when the standard deviation is known is an excellent introduction to how to compute a significance test in the more realistic situation in which the standard deviation has to be estimated.

- The first
step in
hypothesis testing is to specify the null
hypothesis and the alternate hypothesis. In testing hypotheses about µ,
the null hypothesis is a hypothesized value of µ. Suppose the mean
score of all 10-year old children on an anxiety scale were 7. If a researcher
were interested in whether 10-year old children with alcoholic parents
had a different mean score on the anxiety scale, then the null and alternative
hypotheses would be:

H_{0}: µ_{alcoholic}= 7

H_{1}: µ_{alcoholic}≠ 7

- The second step is to choose a significance
level. Assume
the 0.05 level is chosen.

- The third step is to compute the mean. Assume M = 8.1.