Section 12.2: Tests about a Population Proportion AP Statistics Section 12.2: Tests about a Population Proportion

Objective: To be able to conduct a 1 proportion z-test. Recall: Sample proportion = 𝑝 = 𝑋 𝑛 Population proportion = p 1 proportion z-test: (Used to test a claim about a population proportion.) Conditions: SRS Normality: 𝑛 𝑝 0 ≥10 𝑎𝑛𝑑 𝑛 𝑞 0 ≥10 (where 𝑝 0 is the hypothesized proportion from the null hypothesis) Independence: Population is ≥10𝑛

Hypotheses: 𝐻 0 :𝑝= 𝑝 0 𝐻 𝑎 :𝑝> 𝑝 0 ; p< 𝑝 0 ; p≠ 𝑝 0 Rejection Region: I will reject 𝐻 0 if my p-value < 𝛼. OR I will reject 𝐻 0 if z> 𝑧 𝛼 ; z<− 𝑧 𝛼 ; 𝑧 > 𝑧 𝛼 2 Test Statistic & p-value: 𝑧= 𝑝 − 𝑝 0 𝑝 0 ∙ 𝑞 0 𝑛 𝑃 𝑍>𝑧 ;𝑃 𝑍<𝑧 ;2∙𝑃(𝑍> 𝑧 )

**Notice that the standard error of the test statistic 𝑝 0 ∙ 𝑞 0 𝑛 is different from the standard error of the confidence interval for p, 𝑝 ∙ 𝑞 𝑛 . That is because in 𝐻 0 we are assuming that p = 𝑝 0 . In a confidence interval there is no 𝐻 0 and therefore no prior assumption as to what p is. **Technically speaking, since the standard errors are different, we should NOT use the confidence interval to evaluate a two-sided significance test for proportions. 5. State your conclusion in the context of the problem. (2 parts)