ST1131A Introduction to Statistics

The module introduces key ideas underlying statistical reasoning and fundamentals of probability. It serves to introduce students to the various data-analytic operations that can be used to inform leadership in making decisions.

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References

Text

Statistics for Managers Using Microsoft Excel, 3rd edition, Levine, Stephan, Krehbiel & Berenson, ISBN 0130970824, 2002, Prentice Hall, Call# HD30.215 Lev, HD30.215 Lev CD-ROM (Problems are taken from this textbook for tutorials.)

Others

Business & Economic Statistics Using Microsoft Excel, 1^st edition, Black K & Eldredge D L, ISBN 032401726X, 2002, Thomson Learning.

Business Statistics: Decision Making with Data, 1^st edition, Johnson R A and Wichern D W, ISBN 0471592137, 1997, John Wiley, Call# HD30.215 Joh.

Statistical Table

Statistical Tables for Students of Science, Engineering, Psychology, Business, Management and Finance, 4^th edition, Murdoch J and Barnes J A, ISBN 033355859, 1998, Macmillan, Call# QA276.25 Mur.

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Course Syllabus

1. Introduction and Data Collection

Population, sample, statistics, parameter. Types of data and their sources. Design of survey research. Types of sampling methods. Types of survey errors.

2. Presenting Data in Tables and Charts

Frequency distributions table, histograms, polygons. Cumulative distributions tables, ogive. Scatter diagram. Tabulating and graphing univariate categorical data: summary tables, bar and pie charts, the Pareto diagram. Tabulating and graphing bivariate categorical data: contingency tables, side-by-side bar charts. Graphical excellence and common errors in presenting data.

3. Numerical Descriptive Measures

Measures of central tendency: mean, median, mode, geometric mean, and quartile. Measure of variation: range, midrange, interquartile range, variance & standard deviation, and coefficient of variation. Shape of distributions: symmetric, skewed, using box-and-whisker plots. Exploratory Data Analysis. Coefficient of correlation. Pitfalls in numerical descriptive measures and ethical considerations.

4. Basic Probability and Discrete Probability Distributions

Basic probability concepts: sample spaces and events. Operations with Events: union, intersection, complement, and mutually exclusive. Relative frequency & definition of probability, simple probability, joint probability. Conditional probability. Statistical independence, marginal probability. Bayes’s Theorem. Concept of a random variable. Discrete random variable. Discrete probability distribution. Expected value. Variance. Binomial distribution. Poisson distribution. Hypergeometric distribution.

5. The Normal Distribution and Sampling Distributions

Continuous probability distribution. Normal distribution. Assessing normality. Exponential distribution. Sampling distributions of the mean and proportion. Central Limit Theorem.

6. Confidence Interval Estimation

Point and interval estimations. Confidence interval estimations for the mean (s known and unknown). t-distribution. Confidence interval estimation for the proportion. Determining sample size.

7. Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis testing. Null and alternative hypotheses. Type I and II errors. Level of significance. Z-test for the mean (s known). P-value approach to hypothesis testing. Connection to confidence interval estimation. One- and two-tail tests. t-test for the mean (s unknown). Z-test for the proportion.

8. Two Sample Tests with Numerical Data

Comparing two independent samples. Independent samples Z-test for the difference in two means. Pooled variance t-test for the difference in two means. F-test for the comparisons of two variances. Paired sample for the mean difference. Z-test for differences in two proportions.

9. Simple Linear Regression

Types of regression models. Simple linear regression equation. Interpretation of the slope and the intercept. Measures of variation. Assumptions of regression and correlation. ANOVA table. The coefficient of determination (R²) and correlation (r). Residual analysis. Inferences about the slope. Relationship between a t-test and an F-test. Estimation of mean values and prediction of individual values. Strategies for avoiding the pitfalls of regression.