Tests of μ, Standard Deviation Known (1 of 4)


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.

  1. 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:

    H0: µalcoholic = 7

    H1: µalcoholic ≠ 7

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

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