4.4.B—Identify the null and alternative hypotheses for a population mean or population mean difference with unknown σ

Identify the null and alternative hypotheses for a population mean or population mean difference with unknown σ.

• The null hypothesis for a one-sample t-test for a population mean is H:00 ,μμ= in which µ0 is the null hypothesized value for the population mean. A one-sided alternative hypothesis for a one-sample t-test for a population mean is either H:a μμ< 0 or H:a μμ> 0. A two-sided alternative hypothesis is H:a μμ≠ 0.
• The null hypothesis for a population mean difference is H:0 0μd = . A one-sided alternative hypothesis for a population mean difference is either H:a μd < 0 or H:a μd > 0. A two-sided alternative hypothesis is H:a μd ≠ 0.