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# 2003 b

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### 2003 b

2. 2. 2003 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) Formulas begin on page 3. Questions begin on page 6. Tables begin on page 13. 2
3. 3. 2003 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B)Formulas(I) Descriptive Statistics ∑ xix = nsx = 1 n −1 ∑ xi − x 2 3 8 3n1 − 18s2 + 3n2 − 18s2 1 2sp = 3n1 − 18 + 3n2 − 18\$y = b0 + b1 xb1 = 3 ∑ xi − x y i − y 83 8 3 ∑ xi − x 82b0 = y − b1 x 1 x − x yi − y r = n −1 ∑ i sx sy syb1 = r sx 3 \$ ∑ yi − yi 82sb = n−2 1 3 ∑ xi − x 82 3
4. 4. 2003 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B)(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 3Var( X ) = s 2 = ∑ xi − µ x x 82 piIf X has a binomial distribution with parameters n and p, then: n p k (1 − p)n − kP( X = k ) = kµ x = nps x = np(1 − p)µ\$ = p p p(1 − p)sp = \$ nIf x is the mean of a random sample of size n from an infinitepopulation with mean µ and standard deviation s , then:µx = µsx = s n 4
5. 5. 2003 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B)(III) Inferential Statistics statistic - parameterStandardized 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 6 p 1− p 1 + 1 n1 n2 Chi-square test statistic = ∑ 0observed − expected5 2 expected 5