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STAT 270 What’s going to be on the quiz and/or the final exam? Sampling Distribution of X • Large samples, approx N(, N(, • If population Normal, n ) ) n • Small samples, population not normal, use simulation unknown, unless can • But why & when is this useful? • Answer: To assess ( X - ) Sampling Distribution of X 1 -X 2 • Mean is 1- 2 1/ 2 (Var(X ) Var(X )) • SD is 1 2 ^ ^ • What about p1 - p2 ? •Same but use short-cut formula for Var of 0-1 population. (np(1-p)) Probability Models • Discrete: Uniform, Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric. • Continuous: Uniform, Normal, Gamma, Exponential, Chi-squared, Lognormal • Poisson Process - continuous time and discrete time approximations. • Connections between models • Applicability of each model Probability Models - General • pmf for discrete RV, pdf for cont’s RV • cdf in terms of pmf, pdf, P(X…) • Expected value E(X) - connection with “mean”. • Variance V(X) - connection with SD • Parameter, statistic, estimator, estimate • Random sampling, SWR, SWOR Interval Estimation of Parameters • Confidence Intervals for population mean – Normal population, SD known – Normal population, SD unknown – Any population, large sample • Confidence Intervals for population SD – Normal population (then use chi-squared) • Confidence Level - how chosen? Hypothesis Tests • Rejection Region approach (like CI) • P-value approach (credibility assessment) • General logic important … – Problems with balancing Type I, II errors – Decision Theory vs Credibility Assessment – Problems with very big or small sample sizes Applications • • • • • • • • Portfolio of Risky Companies Random Walk of Market Prices Seasonal Gasoline Consumption Car Insurance Grade Amplification (B->A, C->D) Earthquakes Traffic Reaction Times What stats. principles are demonstrated in each example?