- Recognize when a one-sample [latex]z[/latex]-test or a two-sample [latex]z[/latex]-test is needed to answer a research question.
- Complete a two-sample [latex]z[/latex]-test for proportions from hypotheses to conclusions.
Hypotheses
Like any other hypothesis test, the first step for a two-sample [latex]z[/latex]-test for proportions is to clearly state the null hypothesis ([latex]H_{0}[/latex]) and the alternative hypothesis ([latex]H_{A}[/latex]).
hypotheses for a two-sample [latex]z[/latex]-test for proportions
- Null hypothesis: There is no difference between the proportions of the two groups.
[latex]H_0: p_1=p_2[/latex] or [latex]H_0: p_1-p_2=0[/latex]
- Alternative hypothesis: There are three choices between a two-tailed or one-tailed test, depending on the specific research question and the direction of the expected difference in proportions between the two groups.
[latex]H_A: p_1\lt p_2[/latex] or [latex]H_A: p_1-p_2\lt 0[/latex]
[latex]H_A: p_1>p_2[/latex] or [latex]H_A: p_1-p_2>0[/latex]
[latex]H_A: p_1\ne p_2[/latex] or [latex]H_A: p_1-p_2\ne0[/latex]