4.9.B—Identify the null and alternative hypotheses for the difference between two population means

Identify the null and alternative hypotheses for the difference between two population means.

• The null hypothesis for a two-sample t-test for the difference between two population means, µ1 and µ2 , can be written as either H:01 μμ-= 2 0 or H:01 μμ= 2 . A one-sided alternative hypothesis for the difference between population means can be written as either H:a1 μμ< 2 (or equivalently H:a μμ12-< 0 or H:a1 μμ> 2 (or equivalently H:a μμ12-> 0). A two-sided alternative hypothesis for the difference between population means can be written as H:a μμ12≠ (or equivalently H:a μμ12-≠ 0).