文档介绍：AP ?Statistics 201 5 Free -Response Questions ? 2015 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. Visit the College Board on the Web: . AP Central is the official online home for the AP Program: apcentral.. 2015 AP ? STATISTICS FREE-RESPONSE QUESTIONS -2- Formulas begin on page 3. Questions begin on page 6. Tables begin on page 14. 2015 AP ? STATISTICS FREE-RESPONSE QUESTIONS -3- Formulas (I) Descriptive Statistics x i x n ???? 2 1 1 xsxx i n ???????????? 22 12 12 12 11 11 p nsns s nn ??????? 01 ? y bbx ???????? 1 2 ii i x xy y b xx ?????? 01 bybx ?? 1 1 ii xy x xyy r nss ????????????????? 1 y x s br s ????? 2 2 1 ? 2 ii b i yy n s x x ?????? 2015 AP ? STATISTICS FREE-RESPONSE QUESTIONS -4- (II) Probability ()()()() PA B PA PB PA B?????() () () PA B PAB PB ??()EX xp x i i ???μ ?? 2 2 Var( ) x ix Xxp i s????μ If X has a binomial distribution with parameters n and p , then: () (1) n knk PX k p p k ?????????? np x ?μ (1 ) np p x s ??? p p ?μ (1 ) ? p p p n s ?? If x is the mean of a random sample of size n from an infinite population with mean μ and standard deviation , then: s x ?μμ x n s s ? 2015 AP ? STATISTICS FREE-RESPONSE QUESTIONS -5- standard deviation of statistic statistic parameter Standardized test statistic: ???? Confidence interval: statistic critical value standard deviation of statistic ??? Single-Sample Statistic Standard Deviation of Statistic Sample Mean n s Sample Proportion (1 )p p n ? Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 2 1 1 n s ? 2 2 2 n s Special case when 12 ss ? 12 11 nn s ? Difference of sample proportions 1122 12 (1 ) (1 ) p ppp nn ??? Special case when 12p p ??? 1p p ? 12 11 nn ?? 2 observed expected Chi-square test statistic expected ????(III) InferentialStatistics 2015 AP ? STATISTICS FREE-RESPONSE QUESTIONS ? 2015 T