Créer une présentation
Télécharger la présentation

Télécharger la présentation
## c 2 test for independence

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**c2 test for independence**• Used with categorical, bivariate data from ONEsample • Used to see if the two categorical variables are associated (dependent) or not associated (independent)**Hypotheses – written in words**H0: two variables are independent Ha: two variables are dependent Be sure to write in context!**A beef distributor wishes to determine whether there is a**relationship between geographic region and cut of meat preferred. If there is no relationship, we will say that beef preference is independent of geographic region. Suppose that, in a random sample of 500 customers, 300 are from the North and 200 from the South. Also, 150 prefer cut A, 275 prefer cut B, and 75 prefer cut C.**If beef preference is independent of geographic region, how**would we expect this table to be filled in? 90 60 165 110 45 30**Assuming H0 is true,**Expected Counts**Degrees of freedom**Or cover up one row & one column & count the number of cells remaining!**Now suppose that in the actual sample of 500 consumers the**observed numbers were as follows: (on your paper) Is there sufficient evidence to suggest that geographic regions and beef preference are not independent? (Is there a difference between the expected and observed counts?)**Assumptions:**• Have a random sample of people • All expected counts are greater than 5. • H0: geographic region and beef preference are independentHa: geographic region and beef preference are dependent • P-value = .0226 df = 2 a = .05 • Since p-value < a, I reject H0. There is sufficient evidence to suggest that geographic region and beef preference are dependent. Expected Counts: N S A 90 60 B 165 110 C 45 30**c2 test for homogeneity**• Used with a single categorical variable from two (or more) independent samples • Used to see if the two populations are the same (homogeneous)**Assumptions & formula remain the same!**Expected counts & df are found the same way as test for independence. Only change is the hypotheses!**Hypotheses – written in words**H0: the two (or more) distributions are the same Ha: the distributions are different Be sure to write in context!**College Students’ Drinking Levels**The data on drinking behavior for independently chosen random samples of male and female students was collected. Does there appear to be a gender difference with respect to drinking behavior?**Expected Counts:**M F 0 158.6 167.4 L 554.0 585.0 M 230.1 243.0 H 38.4 40.6 • Assumptions: • Have 2 random sample of students • All expected counts are greater than 5. • H0: drinking behavior is the same for female & male studentsHa: drinking behavior is not the same for female & male students • P-value = .000 df = 3 a = .05 • Since p-value < a, I reject H0. There is sufficient evidence to suggest that drinking behavior is not the same for female & male students.**Titanic**Moviemakers of Titanic imply that lower-class passengers were treated unfairly. Was that accurate?**Likelihood of Survival on Titanic?**Ho: C = 109/1318, W = 402/1318, M = 807/1318 Ha: at least one is different 2 = 225.16, df = 2, P(2 > 225.16) = 0.000 Reject Ho and conclude at least one proportion is different.