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AP Statistics Inference Review Chapters 18-25 Remember Your Formulas 1 Proportion: CI = pˆ z 1 Sample or Matched Pairs t-test pˆ qˆ n CI = x t Hypothesis Test: z = pˆ p pq n 2 Proportion: CI = ( pˆ 1 pˆ 2 ) z Hypothesis Test: df s n Hypothesis Test: x tdf = s n 2 Sample t-test: pˆ 1qˆ1 pˆ 2 qˆ 2 n1 n2 ( pˆ1 pˆ 2 ) 0 z = p pool q pool p pool q pool n1 n2 CI: ( x1 x2 ) t df s12 s22 n1 n2 Hypothesis Test: tdf = ( x1 x2 ) 0 s12 s22 n1 n2 Remember PANIC for CI’s and PHANTOMS for Hypothesis Tests Parameter Assumption Name Test and Statistics Interval (Include Formula) Conclusion Parameter Hypothesis (p or mu) Assumptions/Conditions Name Test Test Statistics Obtain P (Include formula and distribution) Make Decision (Never accept Ho State Conclusion (In Context) Name Statistics: n = 50, p-hat = .7, q-hat = .3 Interval: CI .7 1.96 Conclusion: (.7)(.3) 50 Parameter: p = proportion of city workers who are also in the union Hypothesis: Independent: Each person being in The union should be independent Name: One proportion z-test Test Statistics: p-hat = .12, p = .135, q = .865, n = 2000 Obtain P: z Decision: Conclusion: .12 .135 (.135)(.865) 2000 Parameter: Assumptions: Name: 2 Proportion z-Interval Interval: CI (.065 .017) 2.576 Conclusion: (.065)(.935) (.017)(.983) 1000 1000 Parameter: Ps = Proportion of suburban students that failed AP exam Pr = Proportion of rural students that failed AP exam Hypothesis: Ho: Ps = Pr, Ha: Ps ≠ Pr Assumptions: 10%: Both 107 and 143 are less than 10% of rural and suburban students that took AP exam. Name: 2 Proportion z-test Make Decision: Fail to reject Ho Test Statistics: State Conclusion: Obtain P: z (.280 .315) 0 .59 (.3)(.7) (.3)(.7) 107 143 P =.56 Parameter: Name Test: Interval: Assumptions: Random: It is a random selection of days during the year. Nearly Normal: The histogram is roughly unimodal and symmetric Independent: Each car’s speed should be independent 10%: 20 cars is less than 10% of all cars that pass through when the sign is flashing CI 24.6 t19 7.24 20 Conclusion: Parameter: U = average # of hours students watch TV per week from Central High Hypothesis: Ho: U = 13, Ha: U > 13 Assumptions: Name Test: Test Statistics: Obtain P: Nearly Normal: Histogram is roughly unimodal and symmetric. Random: Students were randomly selected Independent: TV watching among students should be independent 10%: 25 students is less than 25% of all students at CHS. Conclusion: Parameter: Assumptions: Name: Interval: CI (15.625 14) 2.131 Conclusion: 3.122 2.532 16 16 Parameter: Um = mean death age of men, Uw = mean death age of women Hypothesis: Ho: Um = Uw, Ha: Um < Uw Assumptions: Name Test: Test Statistics: Obtain P: t71.8 (68.33 78.7) 0 12.492 16.432 48 40 Conclusion: Parameter: Ud = The mean difference in unemployment rate between Australia and UK Assumptions: Assumptions continued: Nearly Normal: Histogram is roughly unimodal and symmetric 10%: 1990 – 2000 represents less than 10% of All of the years Name: Interval: Conclusion: Parameter: Ud = The mean difference in employment rate between Males and Females Hypothesis: Assumptions: Name: Match paired t-test Test Statistics: Obtain P: t7 346.125 0 713.166 8 Make Decision: Fail to reject Ho State Conclusion: