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# 2005 a

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### 2005 a

2. 2. 2005 AP® STATISTICS FREE-RESPONSE QUESTIONS Formulas begin on page 3. Questions begin on page 6. Tables begin on page 12. 2
3. 3. 2005 AP® STATISTICS FREE-RESPONSE QUESTIONSFormulas(I) Descriptive Statistics ∑ xix = n 1 2sx = ∑ xi − x n −1 d i d n1 − 1 s2 + n2 − 1 s2 1 i 2 d isp = d n1 − 1 + n2 − 1 i d iy = b0 + b1 x ∑ xi − x y i − yb1 = d di i 2 ∑ d xi − x ib0 = y − b1 x 1 xi − x FI yi − y Ir = F n −1 ∑ G sx GJ sy J H HK K syb1 = r sx 2 ∑ d yi − yi isb = n−2 1 2 ∑ d xi − x i 3
4. 4. 2005 AP® STATISTICS FREE-RESPONSE QUESTIONS(II) ProbabilityP( A ∪ B) = P( A) + P( B) − P( A ∩ B) P( A ∩ B )P( A B ) = P( B )E( X ) = µ x = ∑ xi pi 2Var( X ) = s 2 x = ∑ d xi − µ x i piIf X has a binomial distribution with parameters n and p, then: p (1 − p) n − k n kP( X = k ) = I F J G K H kµ x = nps x = np(1 − p)µ = p p p(1 − p)s = p nIf x is the mean of a random sample of size n from an infinitepopulation with mean µ and standard deviation , then: sµx = µ x =s s n 4
5. 5. 2005 AP® STATISTICS FREE-RESPONSE QUESTIONS(III) Inferential Statistics statistic parameter -Standardized test statistic: standard deviation of statisticConfidence interval: statistic ± ( critical value standard deviation of statistic ( ∑ ) ) Single-Sample Standard Deviation Statistic of Statistic σ Sample Mean n p(1 − p) Sample Proportion n Two-Sample Standard Deviation Statistic of Statistic Difference of σ1 2 σ2 sample means + 2 n1 n2 Special case when σ 1 = σ 2 1 1 σ + n1 n2 Difference of p1 (1 − p1 ) p (1 − p2 ) sample proportions + 2 n1 n2 Special case when p1 = p2 1 1 p 1− p b g + n1 n2 observed − expected 2 Chi-square test statistic = a f ∑ expected 5