Introductory StatisticsMathematics and Statistics
By the end of this chapter, the student should be able to:
- Interpret the chi-square probability distribution as the sample size changes.
- Conduct and interpret chi-square goodness-of-fit hypothesis tests.
- Conduct and interpret chi-square test of independence hypothesis tests.
- Conduct and interpret chi-square homogeneity hypothesis tests.
- Conduct and interpret chi-square single variance hypothesis tests.
Have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer these questions by conducting a hypothesis test.
You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.
In this chapter, you will learn the three major applications of the chi-square distribution:
- the goodness-of-fit test, which determines if data fit a particular distribution, such as in the lottery example
- the test of independence, which determines if events are independent, such as in the movie example
- the test of a single variance, which tests variability, such as in the coffee example
Though the chi-square distribution depends on calculators or computers for most of the calculations, there is a table available (see [link]). TI-83+ and TI-84 calculator instructions are included in the text.
Look in the sports section of a newspaper or on the Internet for some sports data (baseball averages, basketball scores, golf tournament scores, football odds, swimming times, and the like). Plot a histogram and a boxplot using your data. See if you can determine a probability distribution that your data fits. Have a discussion with the class about your choice.
- Introductory Statistics
- Sampling and Data
- Descriptive Statistics
- Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
- Histograms, Frequency Polygons, and Time Series Graphs
- Measures of the Location of the Data
- Box Plots
- Measures of the Center of the Data
- Skewness and the Mean, Median, and Mode
- Measures of the Spread of the Data
- Descriptive Statistics
- Probability Topics
- Discrete Random Variables
- Probability Distribution Function (PDF) for a Discrete Random Variable
- Mean or Expected Value and Standard Deviation
- Binomial Distribution
- Geometric Distribution
- Hypergeometric Distribution
- Poisson Distribution
- Discrete Distribution (Playing Card Experiment)
- Discrete Distribution (Lucky Dice Experiment)
- Continuous Random Variables
- The Normal Distribution
- The Central Limit Theorem
- Confidence Intervals
- Hypothesis Testing with One Sample
- Hypothesis Testing with Two Samples
- The Chi-Square Distribution
- Linear Regression and Correlation
- F Distribution and One-Way ANOVA
- Appendix A: Review Exercises (Ch 3-13)
- Appendix B: Practice Tests (1-4) and Final Exams
- Appendix C: Data Sets
- Appendix D: Group and Partner Projects
- Appendix E: Solution Sheets
- Appendix F: Mathematical Phrases, Symbols, and Formulas
- Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators
- Appendix H: Tables