Syllabus: Math 130 - Elements of Statistics

3 credits

Department of Mathematics

Millersville University

Catalog Description

Derivation of basic formulas; measures of central tendency and variability; probability and normal curve; sampling and hypothesis testing. No credit toward mathematics major.

Prerequisites

High school algebra or Math 101.

Objectives

1. To introduce students to elementary probability and its applications.
2. To introduce students to some basic methods of statistical analysis.
3. To provide enough statistical training so that students can read research articles, communicate with statisticians, and interpret computer outputs involving means, standard errors, significance levels, confidence limits and other fundamental measures.
4. To introduce students to a statistical computing package (Minitab) and use this package to solve problems in probability and statistics.

Course Outline

1. Introduction
   1. Role of Statistics in Research
   2. Objectives of MATH 130
   3. Two major areas of statistics
      1. Descriptive statistics
         1. central tendency measures - mean, median, mode
         2. measures of variability - range, variance, standard deviation
      2. Statistical Inference
         1. population vs. sample
         2. random samples vs. non-random samples
         3. probability as a tool in making inference
2. Basic Probability
   1. Random phenomena and random experiments
      1. sample spaces and events
      2. combining events (using "or" for union, "and" for intersection)
      3. mutually exclusive events
   2. Definitions of Probability
      1. relative frequency probability
      2. equally likely outcomes probability
      3. mathematical definition of probability
   3. Fundamental Properties of Probability
      1. additive property (mutually exclusive and non-mutually exclusive events)
      2. complement
      3. multiplicative property
         1. tree diagrams
         2. conditional probability
      4. independent events
   4. Counting Theory (optional)
      1. factorials
      2. number of samples possible when sampling a finite population without replacement and not counting order:
         1. properties of binomial coefficients
         2. use of binomial coefficient table
3. Random Variables and probability distributions
   1. Random variables
      1. discrete-values
      2. continuous-values
   2. Mean, variance, and standard distribution of a discrete random variable
   3. Probability distribution functions
      1. Binomial distribution
         1. properties of binomial experiments
         2. calculation of binomial probabilities
            1. using formula
            2. using binomial tables
         3. applications
      2. Normal distributions - standard and others
         1. standard normal table use
         2. calculation of probabilities for any normal distribution
         3. central limit theorem
         4. applications using Central Limit Theorem
            1. variation of sample mean and standard deviation
            2. approximating binomial probabilities
4. Statistical Inferences - basic ideas
   1. Hypothesis Testing - introduction to concepts and terms
      1. null and alternative hypothesis
      2. types of error
      3. alpha-level
      4. beta-level and the power of the test (optional)
   2. Methodology of hypothesis testing
      1. test statistic, critical values and decision
   3. Testing of hypothesis involving one population
      1. tests on mean
         1. large sample, pop. distribution unknown
         2. normal population, sample may be small
      2. test on p of a binomial
         1. large sample
         2. small sample - an exact test probability
      3. test on variance of a normal population (optional)
   4. Testing Hypothesis - involving two populations (time permitting)
      1. independent populations - tests comparing means
         1. large samples, population distributions unknown
         2. normal populations, equal variance, samples may be small
   5. Estimation - confidence limits
      1. one population
         1. mean
         2. p of a binomial
         3. variance (optional)

Suggested Texts

• Just the Essentials of Elementary Statistics, 9th ed., by R.Johnson and P.Kuby. Brooks/Cole, 2005.

General Education Credit

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