1. AGENDA:

2. AP STAT Ch. 14.: X 2 Tests Goodness of Fit Homogeniety Independence EQ: What are expected values and how are they used to calculate Chi-Square?

3. Characteristics of the Chi-Square Distribution: 1. 2. 3. 4. Total are under curve = 1 Skewed right Left Bound at 0 WHY?? Shape depends on df

4. As degrees of freedom increase, the distribution becomes more normally distributed. Larger values of  2, are evidence to reject the H o. WHY?

5.  Three Types of Chi-Square Hypothesis Testing: I. Goodness of Fit ---- expected values must be calculated by hand; use  2 cdf to find p-value  2 cdf( low bound, 100, df) = p-value  Use when you have one population and a theoretical set of proportions you expect to see in each category.

6.  These proportions are used to calculate expected counts.  Calculate (Obs – Exp) 2 /Exp for each cell then add them to get the  2 test statistic. Must state df = k – 1, where k is number of proportions, not sample size. Must record expected counts in table. Data is conveyed in a 1 x n table.

7. Template for Chi-Square Goodness of Fit Test:

9.  Chi-Square Activity #1: Follow the template to run this  2 GOF Problem Use your bag of M & M’s to determine if you believe their claim.

10. Parameters: Inference Test: Hypotheses: Conditions: 1. SRS 2. exp counts > 1 80% of exp counts > 5 p br = the true proportion of brown M & M’s in a bag of M&M’s p y = the true proportion of yellow M & M’s in a bag of M&M’s p r = the true proportion of red M & M’s in a bag of M&M’s p or = the true proportion of orange M & M’s in a bag of M&M’s p g = the true proportion of green M & M’s in a bag of M&M’s p bl = the true proportion of blue M & M’s in a bag of M&M’s Create table then come back to #2!

11. Decision: df = ______  = _____

12.  Chi-Square Activity #2: Follow the template to run this  2 GOF Problem Use your cup (bag) of Skittles to determine if you believe their claim.

13. Parameters: Inference Test: Hypotheses: Conditions: p r = the true proportion of red Skittles in a bag of Skittles p o = the true proportion of orange Skittles in a bag of Skittles p y = the true proportion of yellow Skittles in a bag of Skittles p g = the true proportion of green Skittles in a bag of Skittles p p = the true proportion of purple Skittles in a bag of Skittles Create table then come back to #2! 1. SRS 2. exp counts > 1 80% of exp counts > 5

14. Decision:

15.  ASSIGNMENT: p. 846 – 847 #3, 4

16.  Chi-Square Hypothesis Testing PART 2: I.Goodness of Fit  II.Test of Homogeneity of Populations --- use the  2 test function on the calculator; enter your contingency table in Matrix A.

17. Use when separate surveys are conducted on different populations and you want to test whether they are homogeneous with respect to one variable  Calculate the expected frequencies for each cell using [(row total)(column total)]/grand total *** These values will be found in MATRIX B after you run the  2 test function

18.  Calculate (Obs – Exp) 2 /Exp for each cell then add them to get the  2 test statistic.  df = (row – 1)(column – 1)  Data is conveyed in a contingency table (at least 2 rows and 2 columns)

19. In Class Example:for Chi-Square Test of Homogeneity: p. 866 #15 (refers to p. 855 #11)