1. Chi Square 11.1 Chi Square

2. All the tests we’ve learned so far assume that our data is normally distributed z-test t-test We test hypotheses about parameters of these normal distributions We call these tests “Parametric Tests” 11.1 Chi Square

3. Review What if our data is not normally distributed? Skewed distributions Nominal or ordinal data Then we use “Nonparametric Tests” Tests that do not deal with parameters 11.1 Chi Square

4. Parametric vs. Nonparametric Tests Parametric Tests – tests used to analyze data from which parameters such as the mean, median, and mode can be calculated e.g. reaction time, height jumped, grade on a test, etc. Nonparametric Tests – tests used to analyze data that cannot be described by the mean, median, or mode e.g. letter grades, state of residence, gender. 11.1 Chi Square

5. Parametric vs. Nonparametric Tests Parametric Tests Test hypotheses about some parameter (e.g. about the mean) Nonparametric Tests Test hypotheses about entire distribution 11.1 Chi Square

6. Nonparametric Tests Chi square Nonparametric test to analyze nominal data. Recall – with nominal data, the data consist of mutually exclusive categories that have no order. 11.1 Chi Square

7. Chi Square goodness of fit One variable, 2 or more levels Compare observed data with the expected data Predicted data Based on chance Based on data 11.1 Chi Square

8. f o = observed value f e = expected value d.f. = (rows –1)(columns – 1) 11.1 Chi Square

9. Is there a difference between grade level and soda preference? Soda High School Elementary Total Coke 33 57 90 Pepsi 30 20 50 Sprite 5 35 40 Mist 12 8 20 Total 80 120 200 F e (coke at high school) = (90)(80)/200 = 36 /36/54 /20/30 /16/24 /8 /12 11.1 Chi Square

10. 1.H 0 : The two qualitative variables, grade and soda preference are independent of each other. H A : The two qualitative variables, grade and soda preference are not independent of each other. 2.Use Chi-Square distribution model. 3.Determine endpoints of the rejection region. 4.Compute Chi-Square test statistic. 5.State the conclusion. 11.1 Chi Square

11. χ 2 = 24.68 At the α =.01 for (4 - 1)(2 - 1) = 3 d.f. χ critical = 11.34 24.68 > 11.34, conclude that grade school and high school soda preference are not independent. 11.1 Chi Square

12. http://www.georgetown.edu/faculty/ballc/webtools/web_chi.html

13. Confidence interval for σ 2 A B middle C% of model Right Tail Area for a C% Confidence Interval C% Right of A Right of B 60%.80.20 80%.90.10 90%.95.05 11.1 Chi Square

14. Find an 80 % confidence interval for σ with n = 9 and s = 1.4.90.10 11.1 Chi Square

15. Find an 80 % confidence interval for σ with n = 9 and s = 1.4 11.1 Chi Square

16. Find an 60 % confidence interval for σ with n = 14 and s = 1.03.8.2 11.1 Chi Square

17. Find an 80 % confidence interval for σ with n = 9 and s = 1.4 11.1 Chi Square