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Understanding Sampling Distribution and Probability Models for Effective Exam Preparation

This guide provides an overview of key concepts related to sampling distributions and probability models, essential for success in your upcoming quiz and final exam. It covers large and small sample distributions, the relevance of normality, confidence intervals for population parameters, and hypothesis testing methods. By exploring practical applications and modeling techniques, including the connection between mean, variance, and expected values, this resource offers crucial insights into statistical principles in real-world scenarios, such as market behavior and insurance.

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Understanding Sampling Distribution and Probability Models for Effective Exam Preparation

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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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