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

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*t*-tests

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