University:
Eastern Kentucky University
Course:
STA 230 | Probability and Statistics for Middle Grades Teachers
Academic year:

2020
Views:

263

Pages:

6
Author:

Marilyn James

Formulas for AP Statistics I. Descriptive Statistics ∑ xi 1 x = ∑ xi = n n sx = ŷ = a + bx y = a + bx r = II. 1 ∑ xi − x  yi − y     n − 1  sx   sy  b=r 1 ∑( x − x) i n− 1 2 ∑( xi − )x n− 1 = sy sx Probability and Distributions P (A | B) = P (A ∪ B ) = P (A) + P( B) − P( A∩ B) Probability Distribution Mean Discrete random variable, X µ X = E ( X) =∑ xi P( x)i If 𝑋𝑋 has a binomial distribution with parameters n and p, then: n  n −x P ( X = x) =  px (1− p) x  P( A ∩ B) P ( B) Standard Deviation σ = ∑( x − µ X i µ X = np X ) 2 P( x)i σ X = np (1− p) where x = 0, 1, 2, 3,  , n If 𝑋𝑋 has a geometric distribution with parameter p, then: −1 P ( X = x) =( 1− p) x p µX = 1 σ p X − = 1 p p where x = 1, 2, 3,  III. 2 Sampling Distributions and Inferential Statistics Standardized test statistic: statistic − parameter standard error of the statistic Confidence interval: statistic ± ( critical value)( standard error of statistic) Chi-square statistic: χ 2 = ∑ ( observed − expected) expected 2 III. Sampling Distributions and Inferential Statistics (continued) Sampling distributions for proportions: Random Variable For one population: p̂ For two populations: pˆ1 − pˆ 2 Standard Error* of Sample Statistic Parameters of Sampling Distribution µ pˆ = p µˆ p1 − pˆ 2 = p− p 1 2 p (1 − p) n σ pˆ = σ pˆ1 − pˆ2 = pˆ (1 − pˆ) n spˆ = p1 (1 − p1 ) p2( 1 − p2) + n1 n2 spˆ 1 −pˆ2 pˆ1 (1 − pˆ1 ) pˆ2( 1 − pˆ 2) + n1 n2 = When p 1 = p 2 is assumed: s pˆ 1 −pˆ2  pˆ c (1 − pˆ c)  1 + 1  n2  n1 = where pˆ c = X1 + X2 n1 + n 2 Sampling distributions for means: Random Variable For one population: X For two populations: X −X 1 Standard Error * of Sample Statistic Parameters of Sampling Distribution µ µ X X1 − X2 =µ =µ − µ 1 2 2 σ σ X1 − X2 X = σ σ2 1 = s sX = n n n1 + σ 2 2 2 sX − X = n2 1 2 2 s1 s + 2 n1 n2 Sampling distributions for simple linear regression: Random Variable For slope: b Standard Error* of Sample Statistic Parameters of Sampling Distribution σb = µb = β where σ x = sb = σ σ x n , ∑( x − x) i n 2 where s = and sx = s , sx n − 1 ∑( y − ˆy) i i n−2 ∑ ( x − x) i n −1 2 2 *Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error.

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