Syllabus: Math 235 - Survey of Statistics

3 credits

Department of Mathematics

Millersville University

Catalog Description

A survey of elementary probability theory, estimation, hypothesis testing, and simple regression and correlation. Interpretation of statistical inference in the analysis of data. Emphasis on application in both behavioral and physical sciences.

Prerequisites

Math 151 or Math 160.

Objectives

The objectives of this course are to provide the student with a basic understanding of statistical inference in the areas of estimation, and hypotheses testing. Thus, the student should acquire:

1. An insight into the need and role of statistical inference in the analysis of data.
2. An ability to read and understand technical literature, now rather commonly interwoven with statistical terminology.
3. An understanding of elementary probability theory:
   1. As background for upper level computer science courses.
   2. As a necessary foundation for subsequent courses such as operations research.

Course Outline

1. Introduction
   1. Descriptive and inferential statistics
   2. Populations and samples
   3. Problems for the statistician
2. Statistical Measures of Data
   1. Parameters and statistics; measures of central location
   2. Measures of variation; Chebyshev's theorem
3. Probability
   1. Sample space; events
   2. Operations with events
   3. Counting sample points. (Multiplication rule, permutations, combinations)
   4. Probability of an event; additive rules
   5. Conditional probability; multiplicative rules
4. Distributions of Random Variables
   1. Concept of a random variable
   2. Discrete probability distributions
   3. Continuous probability distributions
   4. Mean of a random variable; mathematical expectation
   5. Variance of a random variable
5. Some Discrete Probability Distributions
   1. Uniform and binomial distributions
   2. Poisson distribution
6. The Normal Distribution
   1. Normal curve; areas under the curve
   2. Applications
   3. Normal approximation to the binomial distribution
7. Sampling Distributions
   1. Sampling distributions of the mean, with and without replacement
   2. Central limit theorem
   3. t distribution
   4. Sampling distributions of the differences of means
8. Estimation of Parameters
   1. Statistical inference; classical methods of estimation; estimating the mean
   2. Estimating the difference between two means (large sample, small sample, paired observations)
   3. Estimation a proportion, and the difference between two proportions
9. Tests of Hypotheses
   1. Statistical hypotheses; testing a statistical hypothesis Type I and Type II errors
   2. One-tailed and two-tailed tests
   3. Tests concerning means (large sample, small sample, paired difference)
   4. Tests concerning properties and the difference between two properties

Suggested Texts

• Statistics, 10th ed., by J. McClave, Dietrich, and T. Sincich. Prentice Hall Inc., 2006.

General Education Credit

This course may be taken for general education credit (G2, Q).

This syllabus was last revised in August, 1997.