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STAT 270

STAT 270. What’s going to be on the quiz and/or the final exam?. Sampling Distribution of. Large samples, approx If population Normal, Small samples, population not normal, unknown, unless can use simulation But why & when is this useful? Answer: To assess ( - ).

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STAT 270

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  1. STAT 270 What’s going to be on the quiz and/or the final exam?

  2. Sampling Distribution of • Large samples, approx • If population Normal, • Small samples, population not normal,unknown, unless can use simulation • But why & when is this useful? • Answer: To assess ( - )

  3. Sampling Distribution of - • Mean is 1- 2 • SD is ^ ^ • What about p1 - p2 ? • Same but use short-cut formula for Var of 0-1 population. (np(1-p))

  4. 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

  5. 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

  6. 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?

  7. 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

  8. 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?

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