STAT 270

1
STAT 270

• Whats 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 conts 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-gtA, C-gtD)
• Earthquakes
• Traffic
• Reaction Times

What stats. principles are demonstrated in each
example?