1 August 22, 1999
Math 3770 - Statistics and Applications
e-Catalog Description:
Introduction to probability, probability
distributions, point estimation, confidence intervals, hypothesis testing, linear
regression and analysis of variance. Math majors may not take this course for credit.
Crosslisted with ISYE 3770.
General Description.
This is an introductory statistical methods
course whose emphasis is on the application of statistical techniques. The main goal of
the study of probability in this course should be the student's appreciation of the role of
the probability density in the calculation of probabilities and the role of transformations
and the underlying population in the determination of the form of the density. Without
formal derivation, the student can be apprised of the important densities which arise
and their use in estimation and hypothesis testing which are the focus of the course.
The assignment of exercises which make use of calculus need not be avoided,
but the primary objective should be to impart an understanding to the student of the
use of statistics in the analysis of data rather than the development of technical
proficiency in things like the computation of means, moment generating functions, or
complicated probabilities.
Lectures
1 through 15,Introduction to probability
- events, sets, probabilities,
simple laws, conditional probability, Bayes theorem, independent events - random
variables, hypergeometric, Binomial, Poisson, geometric, Poisson as an approximation
to the Binomial and the binomial as approximation to the hypergeometric, densities of
(absolutely) continuous random variables as approximations to large population
relative frequency histograms, exponential, Normal, gamma, Weibull - means and
variances - chi square as the square of a normal - several random variables,
independence, sums of independent random variables and reproductive properties
with applications to sums of normals - formulas for covariances, variance of a sum - the
Central Limit Theorem and applications
16 through 23, Estimation
- unbiased, minimum variance -
development of confidence intervals (introduce the t and F distributions and their
properties, including the use of tables, as needed) for means with known variance in
the normal case, large sample confidence intervals for means, small sample confidence
intervals for means, two sample problem analogs and paired differences (an
introduction to blocking), confidence intervals for variances and ratios of variances -
24 through 29, Informal introduction to formal hypothesis testing
- calculation of size and evaluation of the power function - Give one and two
sample tests of hypotheses for normal means and variances with an intuitive
justifications in the normal case, large sample tests of means and proportions, and
plenty of applications problems illustrating the proper selection of the null hypothesis -
The SAS routine PROC TTEST or the output from some other statistical package and its
use can be introduced here.
30 through 34, Analysis of Variance
- Do the one way analysis of
variance for one factor (10.1) and for two factors with and without interaction (11.1,11.2)
- do multiple comparisons lightly or not at all and de-emphasize computational
formulas in favor of using available software in this and the next section. Both DataDesk
and JMP-IN are available to students in the Mac lab, rm. 156, but are single user only.
35 through 42, Regression
- Derivation of the least squares line and
the distribution theory under the null hypothesis, assuming independence, of the test
statistic for the slope - give other important tests and confidence intervals and illustrate
on real data - A good understanding of output of the SAS routine PROC REG ( or some
other canned statistical package) is one goal here. Sections 13.1 and 13.2 can be done if
there is sufficient time. The idea of multiple regression can be conveyed by examples
run on DataDesk or other software, but there is no time to treat this topic further.
Time has been alloted for three exams based upon a 15 week semester.
Text: DeVore, Probability and Statistics for Engineering and the Sciences, Fourth Ed.
Approximate Coverage:
Chapter 2.
Chapter 3. Do all but negative binomial (do geometric instead)
Chapter 4. Do only the Weibull from section 4.5 and 4.6 is optional
Chapter 5.
Chapter 6. Do only unbiasedness of sample averages for the mean and sample variance
for the population variance.
Chapter 7. Prediction intervals should be omitted
Chapter 8. Treat sample size determination here lightly or not at all.
Chapter 9. Omit treatment of testing normal means when s 21 s 22
Chapter 10. Do only section 10.1.
Chapter 11. Section 11.1 and 11.2 except omit multple comparisons and beyond
Chapter 12. 12.1, 12.2, 12.3, 12.4 - Do all but prediction intervals.
Chapter 13. 13.1, 13.2 if there is time