Syllabus Rev. 12/30/09

Prerequisite: A course in  statistics, or MAC 2312, or high school equivalent.

Terms offered: Fall

Textbook: An Introduction to Statistical Methods and Data Analysis, 6th edition, by R. Lyman Ott and Michael Longnecker, 2001. Duxbury.

Note: Statistical software packages will be used in this course..

Topics:

• Introduction. The science of statistics. Basic terms and concepts. Applications of statistics. The collection and management of data.



• Descriptive Statistics. Description of qualitative and quantitative data. Use of frequency tables, graphs (bar charts, histograms, stem-and-leaf displays, dot plots, box plots, etc) and numerical measures (centrality, variability, relative standing). The empirical and Tchebyshev's rules.



• Probability. Basic terms and concepts. Event relations. Venn diagrams. Probability laws. Conditional probability and independence. Bayes' formula.



• Random variables and probability distributions. Definition of random variable. Types of random variables. Examples. Discrete probability distributions. The binomial distribution. Continuous probability distributions. The normal distribution. The uniform and exponential distributions (optional).

• Sampling distributions. Random sampling. Sampling distribution: definition and examples. Sampling distribution of mean. The central limit theorem for means and sums. The normal approximation to the binomial.



• Inferences about the central value of a population. Introduction. Estimation of and sample size determination. A statistical test for and sample size determination. The observed level of significance of a test. Inferences about the normal mean. Inferences about the median M.



• Inferences about the central values of two populations. Introduction. Inferences about the difference of two means. Cases of independent and matched samples. Non-parametric alternatives: Wilcoxon Rank-Sum (Mann-Whitney U-test) and Wilcoxon Signed Rank tests. Sample size determination.



• Inferences about population variances. Introduction. Estimation and test of hypothesis about a population variance. Estimation and test of hypothesis about two population variances. Comparison of more two population variances.



• Categorical Data Analysis. Introduction. Inferences about one and two binomial proportions. Multinomial distribution and chi-square goodness-of-fit test. Poisson distribution and goodness-of-fit test. Contingency tables for two categorical variables: Chi-square tests of independence and homogeneity.