1. The Chi-Square Distribution  Chi-square tests for ….. goodness of fit, and independence 1

2. Hypothesis Tests (also called “Tests of Significance”) Standardized test statistic Use “HCCC” for writing FR answers that involve Tests of Significance: H: Write the Hypotheses. Be sure to define any parameter used in them. C: What distribution Can I use? Address each one of the Conditions precisely. C: Do the Calculations – either by hand or on your calculator. C: Write a two-sentence Conclusion. 2

3. As always, the structure of the Hypothesis Test does NOT change. Conclusions should always be in the context of the problem. 3

4. Chi-Square Tests – 2 types Goodness of Fit - testing a claim about the distribution of a categorical variable in a single population Independence – testing to determine whether there is an association between two variables 4

5. Conditions in order to be able to use the Chi-Square Distribution 1.The data come from random samples or random assignment to treatments. 2. All expected counts are at least 5 – be sure to show the expected counts. 3. Independent observations 5

6. Chi-square Goodness of Fit Test This test begins with a claim about the distribution of a single categorical variable (stated as a list of probabilities or proportions), and you are testing to see if the claim is correct. Hypotheses: Ho: Specified distribution is correct (probabilities or proportions are correct as stated) Ha: Specified distribution is not correct (some probabilities or proportions are incorrect as stated in the null hypothesis) 6

7. Chi-Square Goodness of Fit Test Example: “According to one genetics theory, half of the population should have brown eyes, and the other half evenly split between blue eyes and green eyes. “A random sample of 60 people results in 34 browns, 15 greens, and 11 blues. Does this sample provide good evidence for the theory?”  See page 4 of the packet, #19.  Correct answer: B 7

8. The Calculation for GOF: Degrees of freedom = # of categories - 1 8

9. Chi-Square Test of Independence You are given a two-way table showing counts for two characteristics for a single sample. Hypotheses: Ho: 2 variables are independent (or no association between the variables) Ha: 2 variables are not independent (or there is an association, or they are related to each other) (one of these coming up in the packet in a minute…) 9

10. Good Luck! 10