Mathematics 363
Introduction to Statistical Methods
Fall 2016
Exam Overview
Topics for Exam 1
- Displaying data visually –
bar charts, segmented bar charts, histograms, boxplots, empirical
cumulative distribution function, empirical survival function, time plots,
scatterplots, explanatory and response variables
- Displaying data in tables –
marginal distributions
- Summarizing one dimensional data
numerically – mean, variance, standard deviation, five number
summary, quantiles, standardized variables
- Summarizing two dimensional data
numerically – covariance, correlation, linear regression, fit,
residuals, extrapolation, non-linear transformations
- Producing data –
observational study, natural and randomize controlled experiments
- Principles of experimental design
– issues with control, factors, levels, simple and stratified random
samples
- Axioms of probability –
axioms, simple consequences of the axioms, conditional probability, law of
total probability, Bayes formula, independence
- Random variables –
distribution functions, mass function for discrete random variables,
density function for continuous random variables, their properties and
their relationships
- Simulating random variables
– discrete random variables using sampling from a distribution,
continuous random variables using the probability transform
- Expected values – laws of
the unconscious statistician, computing means and variances from the mass
or density function.
- Families of random variables –
review but do not focus on memorizing formulas
Exam 1 Brief Answers
Topics for Exam 2
- Law of large numbers and Monte Carlo
integration
- Central limit theorem for sums and
sample means arising from a simple random sample, estimation of
probabilities using the z-score
- Delta method – normal
approximation for single and multivariable functions of sample means
- Method of moments estimation
- Maximum likelihood estimation
- Interval estimation –
confidence intervals
- Issue associated with hypothesis
testing – null and alternative hypotheses, type I and type II
errors, significance level and power.
- Likelihood ratios – Neyman-Pearson framework
- Composite hypotheses – power
function, p-value
- One and two sample proportion
tests
- One and two sample z procedures
- t-procedures – one
sample, matched pairs, two sample t-tests
Exam 2 Brief Answers
Additional Topics for Final Exams
- Chi-square procedures – G-test,
determining degrees of freedom
- One way analysis of variance
– F statistics, numerator and denominator degrees of freedom,
confidence intervals
Final Exam Brief Answers
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