MAT 1430 Syllabus

Catalog Course Description

To introduce statistical concepts and methods useful in analyzing problems in all areas of business and economics.  In addition to learning the concepts, applications will be addressed in: Descriptive Statistics, Discrete and Continuous Probability Distributions, Sampling Distributions, Confidence Intervals, Hypothesis Testing, and Regression Analysis.

Objectives

The purpose of this course is to provide the students with a sound conceptual and practical introduction to statistics and its applications in the business and economic fields.  Upon completion of the course, a student will be able:

  • To recognize business situations that require the use of statistical tools of analysis.
  • To select and execute the appropriate statistical tool for a specific business situation.
  • To develop critical judgment and decision-making ability through the use of quantitative tools and statistical software.
  • To address ethical issues when presenting and interpreting statistical information.

Topical Coverage

  1. Numerical and Graphical Summaries
  2. Probability Distributions
  3. Methods of Inferential Statistics
  4. Regression and Correlation Analysis
TOPIC CONTENT Estimated Coverage
Descriptive Statistics
  • Types of Variables (levels of measurement)
  • Data Collection and Presentation
    • Types of Sampling Methods
    • Tables and Charts for Categorical Data (summary, bar, pie)
    • Tables and Charts for Numerical Data
      • Ordered Array
      • Steam-and-Leaf
      • Frequency Distributions (histogram)
    • Cross Tabulations
      • Contingency Tables
      • Side-by-side bar charts
    • Scatter Plots and Time Series Plots
  • Numerical Descriptive Measures
    • Measures of central tendency (mean, median, mode)
    • Measures of dispersion (range, quartiles, interquartile range, variance, standard deviation)
  • Shape of a distribution (skewness, box-and-whisker)
  • Covariance between two variables
  • Applications of mean with standard deviation
    • Standardized (Z) scores
    • Empirical Rule
    • Chebyshev's Rule (optional)
3 weeks
Probability and Probability Distributions
  • Basic Probability Concepts - classical, relative frequency and subjective probabilities
  • Discrete Probability Distributions
    • Probability Distribution for a Discrete Random Variable
    • Expected value of a probability distribution
    • Standard deviation of a probability distribution
    • Binomial Distribution
    • Poisson Distribution (optional)
  • Continuous Probability Distributions
    • Normal Distribution
1 1/2 weeks
Sampling Distributions
  • Random Sampling
  • Sampling Distributions of the Mean and Proportions
  • Central Limit Theorem
1/2 week
Confidence Interval Estimation
  • Confidence Interval Estimation for one Mean (z and t distribution)
  • Confidence Interval Estimation for one Proportion
  • Sample size estimation
1 week
Hypothesis Testing
  • Hypothesis tests involving one mean or proportion
  • Introduction to Type I Error, Type II Error, p-value
2 weeks
Simple Linear Regression and Correlation Analysis
  • Interpretation of slope and intercept
  • The least-squares method
  • Standard error of the estimate
  • Coefficient of determination and correlation
  • Estimation and testing of regression parameters
  • Residual analysis
1 1/2 weeks
Multiple Regression and Model Building
  • Multiple regression model
    • Significance tests in multiple regression
      • Test of the overall significance of the model
      • Test of the net regression coefficients
    • Categorical explanatory variables (dummy variables) and interaction terms
    • Multicollinearity
2 weeks
Hypothesis Testing II
  • Chi-Square Test
    • Test for Difference of two proportions
    • Test for differences among more than two proportions
    • Test of Independence
    • Test of Goodness-of-Fit
  • Hypothesis tests involving two sample means, proportions or variances (optional)
  • Analysis of Variance
    • One-way analysis of variance
    • Multiple comparisons
  • Nonparametric methods (optional)
2 weeks

Contact Information

Department of Mathematics & Statistics
SAC Room 305
Villanova University
800 Lancaster Avenue
Villanova, PA 19085 
Tel: 610.519.4850
Fax: 610.519.6928
Email: math@villanova.edu

Chair:
Dr. Douglas Norton

Staff:
Marie O'Brien, 610.519.4809
Lorraine McGraw, 610.519.4850

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