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Final

# 2320CHEATSHEETFORFINAL-1.pdf

6 Pages
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School
Department
Course
Professor
Henry Bartel
Semester
Fall

Description
ADMS2320 Formula Sheet Graphing and Numerical Descriptive Measures: Range ApproximateClass Width≈ Number of Classes Sturges’ Rule: Number of Classes = 1 + [ln(n)]/[ln(2)] ≈ 1 + 3.3[log10n)] Measure Population Sample N n Mean ∑ x1 ∑ x 1 ▯ = i=1 x = i=1 N n N n Variance x − ▯ 2) (x − x 2) 2 ∑ i 2 ∑ i σ = i=1 s = i=1 N n−1 Variance N 2 n 2     (Short-cut N ∑ x i n ∑ x i Formula) x 2−  i 1  x 2−  i 1  2 ∑i 1 i N 2 ∑i 1 i n σ = s = N n −1 Standard σ = σ 2 s = s 2 Deviation Coefficient of σ s Variation CV = cv = ▯ x Covariance N n ∑ (xi− ▯ x(yi− ▯ y ) ∑ (xi− x y i y ) i=1 i=1 σ xy= sxy= N n−1 Covariance  N  N   n  n  (Short-cut ∑ x i∑ y i  ∑ x i ∑ y i N  i 1  i=1  n  i 1  i=1  Formula) ∑ xiyi− ∑ x ii− σ = i 1 N s = i 1 N xy N xy n −1 Correlation σ xy s xy Coefficient ρ = r = σ x y s x y 1  n n Geometric Mean: r = g ∏ (1+ rt ) −1= n(1+ r11 )(r2K 1 + rn(−1 )  = 1  Range = Largest Observation – Smallest Observation th P Location of P Percentile: L = P (n +1 ) 100 THIS FORMULA SHEET IS NOT TO BE REMOVED FROM THE ROOM AND MUST BE SUBMITTED WITH THE EXAMINATION. Probability: n ∑ P(xi = 1 = 1 Joint Probability: P(A and B) Conditional Probability: P(A|B) = P(A and B)/P(B) Multiplication Rule: P(A and B) = P(B)P(A|B) = P(A)P(B|A) Addition Rule (Union): P(A or B) = P(A) + P(B) – P(A and B) C Complement Rule: P(A ) = 1 – P(A) Independence: P(A|B) = P(A) or P(B|A) = P(B) Bayes’ Law: P A ×P BA ) P A i = ) i i P A 1P BA + 1 A )( 2 ×P BA 2 +L) + P Ak ×P BA k ) = P (AiandB ) P A 1ndB + P A an2B + L + P AkandB ( ) Random Variables: Expected Value: E(X) = ▯ =∑ xP(x) all x 2 2 2 2 Variance: V X = σ = ∑ (x -▯ P x = ∑ x P x −▯ all x all x Standard Deviation: σ = σ2 Laws of Expected Value: E(c) = c E(X+c) = E(X) + c E(cX) = cE(X) 2 Laws of Variance: V(c) = 0 V(X+c) = V(X) V(cX) = c V(X) Binomial Probability Distribution: n! x n−x To compute probabilities: P(x = x!(n− x !) 1−p ) for x = 0, 1, 2, …, n Expected Value (Mean): ▯ = np Variance: σ = np 1−p ) 2 Standard Deviation σ = σ = np 1−p ) THIS FORMULA SHEET IS NOT TO BE REMOVED FROM THE ROOM AND MUST BE SUBMITTED WITH THE EXAMINATION. Normal Distribution: X −▯ Standard Normal Values: Z = σ Sampling Distributions: Sampling Distribution of the Sample Mean: 2 σ 2 σ2 σ If X is normal,X is normal. If X is ▯ x ▯ σ x σx= = nonnormal, X is approximately normal n n n for sufficiently large sample sizes. X −▯ Standardizing the Sample Mean: Z = σ n Sampling Distribution of a Proportion: EP = p V P = σ = p(1−p ) σ = p 1−p ) p n p n ˆ Standardizing the Sample Proportion: Z = p−p p 1−p n ) Sampling Distribution of the Difference between Two Means: 2 σ1 σ 2 σ 1 σ 2 ▯ 1 −2= ▯1−▯ 2 σ 1 2x= + σx1−2 = + n1 n2 n 1 n 2 ( ) Standardizing the Difference Between Two Sample Means: Z = X 1 X 2 −(▯1−▯ 2) σ2 σ2 1 + 2 n1 n2 Confidence Interval of the Mean, Standard Deviation known x ± z σ α / 2n P  − z σ < X < ▯ + z σ  = 1− α α/2 n α/ 2 n   THIS FORMULA SHEET IS NOT TO BE REMOVED FROM THE ROOM AND MUST BE SUBMITTED WITH THE EXAMINATION. 2 ▯ p p )2 − 2 Case 2 2 p (1 n 2    p − 2 p 2     1p 2 − (1 n + estimate estimateˆ 1 n 1 2 1 ) + (p p p to to p(1 Z test & ˆ2 1 1 − + 1& 2 − n1 2    ˆ p n ) )1 (1 σ W Nominal estimator of p1 p)  ˆp p p Size / Size / p ˆ 2 2 − − 1 α W α Case 1( − x n 1 (1 n Case / z       p(1 + + ˆ( ˆ1 zα = = ˆ 1 1 p for ± Samplen Sample n x n )2 = = = p z ˆp z −1 2 2 2 p s n Estimator 2 1+ 1 s n Data Type 1, 2, 2 Compare 2 Populations 2, ν α 1 / 2/ t 22 α α ) 2/       x σ 2 1 2 2 2 1 2 2 2, 1, − s s s s 2, 2, 1 test &       1 / / (x F = = 2 1 2 2 α α 2
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