- 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.
Evidence and Conclusion
We use the P-value to make a decision. The P-value helps us determine if the difference in proportions seen in the data is statistically significant or due to chance. One of two outcomes can occur.
- One possibility: The difference in sample proportions from the data is extremely unlikely. In this case, there is only a small chance that proportions from random samples differ more than what we observed in the data. So the probability (the P-value) is small, suggesting that the data did not come from populations with the same proportions. We view this as strong evidence against the null hypothesis. We reject the null hypothesis in favor of the alternative hypothesis.
- The other possibility: The difference in sample proportions observed in the data are fairly likely (not unusual). In this case, it is not surprising to see proportions from random samples with larger absolute differences than we observed in the data. The probability is large enough that we don’t think the data is unusual. It could come from populations with the same proportions. A large P-value suggests that we do not have evidence against the null hypothesis, so we cannot reject it in favor of the alternative hypothesis.
Step 1: Under Enter Data, select the Number of Successes option.
Step 2: Input the relevant data for the study.
| Commonly White Names | Commonly Black Names | Total | |
|---|---|---|---|
| Called Back | 246 | 164 | 410 |
| Not Called Back | 2199 | 2281 | 4480 |
| Total | 2445 | 2445 | 4890 |
Step 3: Under the Type of Inference, select Significance Test and select the appropriate alternative hypothesis.