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Probability distribution

chapter 11

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AP Statistics Chapter 11 Outline 11.1 Chi-Square Goodness-Of-Fit Tests Chi-Square Statistic The chi-square statistic is a measure of how far the observed counts are from the expected counts: Where the sum is over all possible values of the categorical variable The Chi-Square Distribution The chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A particular chi-square distribution is specified by giving its degrees of freedom. The chi-square goodness-of-fit test uses the chi-square distribution with degrees of freedom = the number of categories - 1. The Chi-Square Goodness-of-Fit Test

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Data--Types of Variables Categorical A variable that names categories (whether with words or numerals) Eye Color (brown, blue, green), T-shirt size (large, medium, small), type of vehicle Quantitative A variable that are numerical values taken from an individual Weight (117 lbs, 170 lbs, 253 lbs) School administrators collect data on students attending the school. Which of the following variables is quantitative? B) class (freshman, soph., junior, senior) D) whether the student is in AP classes C) whether the student has taken the SAT A) grade point average E) none of these Ways to display categorical data Frequency Table ? lists categories and counts for each Class Count First 325 Second 285 Third 706 Crew 885 COUNTS! Ways to display categorical data
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