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keyconcepts - STATISTICS 211 HONORS 2007 PROF EMANUEL...

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STATISTICS 211 HONORS 2007 PROF EMANUEL PARZEN KEY CONCEPTS ONE SAMPLE STATISTICAL INFERENCE 10/31 0.Population Parameters \mu, p Estimators from sample \mu\hat, \p\hat Denote standard error by S.E.; derive formulas from SONG OF SUMS for mean, variance of sum of random variables 1.Continuous data summary of quantitative variable Y n M(Y) S SE(sample mean) MIN Q1 Q2 Q3 MAX 2. Continuous data quantile diagnostics symmetry outliers 3. 0-1 data summary of “success-failure” variable N K p\hat=K/n SE(p\hat) for C.I. SE(p_0) to test H_0 4. Population quantile Q(P;Y), 0<P<1, of continuous variable Y Pr[Y<Q(P)]=P, Quantile is Prediction interval endpoint function since Pr[ Q(\alpha/2;Y)<Y<Q(1-(\alpha/2);Y)]=1-\alpha 5. Standard Distributions notation Z=Normal(0,1) ; W Exponential(1) Normal(mean \mu, standard deviation \sigma)=\mu+\sigma Z CHISQ(n-1) Chi-squared; CHIAV(n-1)=CHISQ(n-1)/(n-1) STUDENT(n-1)=Z/sqrt(CHIAV(n-1)); F=CHIAV(m-1)/CHIAV(n-1) Binomial(n,p); Normal approximation Central Limit Theorem for large sample distribution of sum 6. Action strategy for comprehensive analysis of sample steps S I E V
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