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Final

# Formula Sheet Final Exam Page 2.doc

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York University
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Chapter 5: Simple Random Sampling (equal chance) | Stratified Random Chapter 15 Analysis Of Variance (ANOVA): Three Interval Data Sampling (male40% + female60%) | Cluster Sampling (divide into blocChapter 12: Inference about a Population when σ is unknown  use t-test p 1 p ) =1p − p 1 2  Sample Error: diff. result for diff samples. Sample Size  Sample t-test only valid when the histogram is NOT extremely nonnormal. n1= 4, n2= 4, n3= 4 Non-sampling Error: Due to data acquisition, non-response, and selection bias. Sample Size  Non-sample Error NOT   Sampling distributiPn ois appr. normal when np > 5 & n(1–p) ≥ 5 x 1 2.25, x2= 3.25, x3= 5.75 2 2 Chapter 13 Comparing Two Populations: Dif. btw 2 mean/prop. | ratio o2 tw∑ S x − ( ∑ x) / n 2 2 Chapter 9 Sample Distribution: X is nXrmalis normal | If X is Non-  Large d.f.= large sample sizes  more infor. by producing more pow1rful tests = 2.25, s 2 2.92 s3= 3.92 normal  X is appr. normal distribution for n230 | 2arger sample  closer toe II error probabilities) and narrower confidence interval estimation. n −1 E(X ) = μ x = μ =V(X∑ =σ =σ xn σ xσ  d.f 1σ2=σ ) ≥ 1.f2 (σ ≠σ ) so equal variances is more efficiency. 9 +13 + 23 normal. ˆ ˆ ˆ x = = 3.75  Sample Mean: Proportion:P 1 P 2 is appr. normal wh1n 1 5 4 + 4 + 4  Finite Population: σ 2 = x P (x) − μ 2 ˆ ˆ ˆ 2 p1(1− p ) 1 p2(1− p ) 2 Rule of thumb: Pop. Size > 20 Sample size  omit correction factor n 11 − P ) 1 P ≥ 2 n 21 −V ( p 1 p ) 1 σ2 p1− 2 = H :0μ = 1 = μ 2 3 H 1 At least two means differ ( ) ( N − n ) /( N − 1) n1 n2 2 SST = ∑ n jx −jx ) = 4(2.25 - 3.75) + 4(3.25 - 3.75) + 4(5.75 - 3.75)  Z-test StatistZ =: X − μ P(μ − Z σ < X < μ + Z σ ) =1−α  E.g. σ = 2, μ=12 σ / n α /2 α /2 SSE = (n − 1)s 2 =(4 1)(2.25) + (4 1)(2.92) + (4 1)(2.92)  Prob. of 1 cells = 10 or less:  x − μ 10 −12  n ∑ j j  Prob. Mean of 4 cells = 10 or less:  <  = P(Z ≤ −1) = .5 − 3413 = .1587 ANOVA table Prob. of Total 4 cells = 40 or less:  σ x − μ 2 10 −2  Source d. f. Sum of Squares Mean Square  Prob. All 4 cells = 10 or less:≤10) =4P  <  = P(Z ≤ −2) = .5 − 4771 = .0228 SST 26 [P(x ≤10) ] = (.187) = .000ˆ 2 / 4  Treatments k–1 = SST = 26.00 MST = = = 13  ProportionE (P ) = μ p (P) = σ ˆ = p(1 ˆ p) / n(1 − p) / n 2 k −1 3 −1 ˆ P P n  Z-Stat for ProportZ =: E.g. 80% agree(p), ask 350(n), P<75%=? n–k = SSE 24.25 ˆ p (1 − p ) / n Error 9 SSE = 24.24 MSE = = = 2.6944  P − p .75 − .80  n − k 12 − 3 P (P < .75 ) = P  < 2 = P (2 < −2.34 ) = .5 − .4904 = .0096 n–1 = SS (Total) =  p(1 − p) / n (.80 )(1 − .82 ) / 350σ 1 σ 2 Total 11 50.25 V (X −1X ) =1σ x1−x2 = +  Two Mean: E(X − 1 ) = μ1 x −x = μ −1μ 2 n 1 n 2 Rejection region: F α ,k −1,n − k F .05 ,2,9= 4.26 1 2  Z-Stat for two Means: (X −1X ) − 2μ − σ )1 = 2 (σ / n ) + (σ / n ) The Value of Test Statistic:ST 13 Z = 2 x12x2 1 1 2 2 F = = = 4.82 (σ 1 n )1+ (σ / n2) 2 MSE 2.69 Conclusion: Reje0t H , there is enough evidence to conclude that there are Chapter 10 Estimator: appr. Pop. Parameters from Sample Xtatistic. e.g. differences in the number of job offers between the three MBA majors. μ  SST (Sum of Squares for Treatments) – between-treatments variation  Point Est.  single value – P(x)=0, sample n , Not reflect to Parameter value  Larger SST  larger variatiXn b support 1 | SST = 0  Xll  Interval Est.  range of values are equal  Desirable: Unbiasedness ( ), Consistency ( , n , variance )  SSE (Sum
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