1. Chapter 11: Chi–Square and F Distributions Section 1: Chi-Square: Tests of Independence

2. Chi–Square Distribution - Greek letter “Chi”  Chi-Square denoted by  graph is not symmetrical  depends on degrees of freedom  as df increase, graph becomes more symmetrical Chi-Square Test of Independence – used to determine whether two characteristics are related

3. Formulas E = df = (r -1)(c – 1)

4. Example  Use a chi-square test to determine whether there is a relationship between students’ political views and their opinion about a controversial issue. Use a 5% level of significance H o : Political view and opinion are independent H 1 : Political view and opinion are related

5. Contingency table DemocratRepublicanIndependent approve101520 disapprove9216 undecided8218

6. Solution OE (O – E) (O – E) 2 (O – E) 2 /E 1012.15-2.154.62250.3805 158.556.4541.60254.8658 2024.3-4.318.490.7609 97.291.712.92410.4011 25.13-3.139.79691.9097 1614.581.422.01640.1383 87.560.440.19360.0256 25.32-3.3211.02242.0719 1815.122.888.29440.5486 11.102