STAT 111 Lecture Notes - Lecture 18: Statistic, Test Statistic

• School: University of Vermont
• Department: Statistics
• Course: STAT 111
• Professor: Jacob William Martin

Document Summary

Section 7. 1 chi-square goodness-of-fit test for a single categorical variable. Multiple categories: we know how to test a proportion for a single category of a categorical variable. H0 : p = . 3 ha : p . 3. H0 : pa = 0. 2 pb = 0. 3 pc = 0. 3 pd = 0. 1 pf = 0. 1. Ha : at least one pi is wrong. We need a test statistic (single number) that combines all the comparisons. This is known as a chi-square statistic for comparing counts of a categorical variable. Each of the expected counts are at least 5: df = number of categories 1, always use the right tail to find a p-value. Even though the alternative hypothesis implies a two-tailed test. Remember we squared the differences everything is positive! Goodness of fit: a 2 test for goodness-of- fit tests whether the distribution of a categorical variable is the same as some null hypothesized distribution.