- Complete a two-sample [latex]t[/latex]-test for dependent population means from hypotheses to conclusions
Hypothesis Testing for Dependent Samples
Let’s conduct the hypothesis test for the difference in drivers’ reaction times when they are using a cell phone as opposed to when they are not using a cell phone.
null and alternative hypotheses
A dependent or paired [latex]t[/latex]-test compares the mean of the differences, [latex]\mu_d[/latex], to a hypothesized value, which is often [latex]0[/latex], but not always. Thus, a dependent [latex]t[/latex]-test is the same as a one-sample [latex]t[/latex]-test performed on the difference variable, [latex]d[/latex].
In summary, where [latex]k[/latex] is the value of the null hypothesis, we have:
| Null Hypothesis for Independent Samples | Null Hypothesis for Dependent Samples |
| [latex]H_0: \mu_1-\mu_2=k[/latex] | [latex]H_0: \mu_d=k[/latex] |
| Alternative Hypothesis for Independent Samples | Alternative Hypothesis for Dependent Samples |
| [latex]H_A: \mu_1-\mu_2>k[/latex] | [latex]H_A: \mu_d>k[/latex] |
| [latex]H_A: \mu_1-\mu_2 \lt k[/latex] | [latex]H_A: \mu_d \lt k[/latex] |
| [latex]H_A: \mu_1-\mu_2 \ne k[/latex] | [latex]H_A: \mu_d \ne k[/latex] |
It is always important to check the assumptions of a test before you perform any calculations.