Lesson 2: 9.2 Tests About a Population Proportion
Duration of Days: 3
Lesson Objective
Students will be able to perform a one-sample z-test for a population proportion p, including checking conditions, calculating the test statistic, determining the P-value, and making a conclusion.
1. How is a "test statistic" different from a "statistic"?
2. Why do we use the null proportion in our standard deviation formula instead of the sample proportion?
3. What is the difference between a one-sided and two-sided P-value?
AP Stats CED: SRE-2.A (Conditions for p), SRE-2.B (Calculating z and p-value for p), SRE-2.C (Conclusions). Common Core: HSS-IC.B.5.
Description
This section formalizes the 4-Step Process (State-Plan-Do-Conclude) for significance testing. Students learn the test statistic formula. They must check the Random, 10%, and Large Counts conditions, noting that Large Counts must be verified using the null proportion.
Purpose
To provide a rigorous, standardized method for testing claims about categorical data. This allows researchers to distinguish between "sampling variability" and a "statistically significant effect."
DOK Level
Level 3 (Strategic Thinking): Students must correctly link the alternative hypothesis to the calculation of the P-value (lower tail, upper tail, or two-tailed) and interpret the final result as evidence (or lack thereof) for a specific claim.
Struggling Learners: Use a "Directional Arrow" chart.If Ha: p > p0, shade the Right tail. If Ha: p < p0, shade the Left tail. If Ha: p not equal to p0, shade Both tails and multiply by 2.
Advanced Learners: Have them compare a 95% confidence interval and a two-sided significance test at alpha = 0.05 for the same data. Challenge them to explain why the two methods will always lead to the same conclusion regarding the null hypothesis.
ELL Learners: Provide a "Conclusion Script" with blanks."Since our P-value is [less/greater] than alpha, we [reject/fail to reject] H0. We [have/do not have] convincing evidence that [context of Ha] is true."
Quiz