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# slide11 - Chapter 11 Chi-Square χ 2 Tests Bin Wang 1 The...

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Unformatted text preview: Chapter 11: Chi-Square ( χ 2 ) Tests Bin Wang * April 20, 2009 1 The Chi-Square Distribution 1.1 Properties of the chi-square distribution Definition 1.1 (Chi-square distribution) The chi-square distribution • has one parameter: the degrees of freedom, df . The chi-square distribution skews to right for small df and becomes more symmetric for large df . • assumes non-negative values. The entire distribution curve lies to the right of the vertical axis. 1.2 Use the chi-square distribution table 1. Given the df and area of the tail, find the χ 2 value. Example 1.1 For example, if df = 7 and the area of the right tail is . 10 , find the χ 2 value. Answer: 12 . 017 * This lecture notes is first created on April 20, 2009. If you have questions, please contact me via e-mail: [email protected] or phone: (251) 460-6264 ext 2626. 1 Example 1.2 For example, if df = 7 and the area of the left tail is . 10 , find the χ 2 value. Answer: 2 . 833 2 2 A Goodness-of-fit Test Definition 2.1 (Multinomial Experiment) An experiment is called a multinomial ex- periment if 1. it consists of n identical trials (repetitions); 2. each trial results in one of k possible outcomes, k > 2 ; 3. the trials are independent; 4. the probabilities of the various outcomes remain constant for each trial....
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## This note was uploaded on 02/05/2012 for the course ST 210 taught by Professor Wangs during the Fall '09 term at S. Alabama.

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slide11 - Chapter 11 Chi-Square χ 2 Tests Bin Wang 1 The...

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