2. Seven Steps for Doing  2 1) State the hypothesis 2) Create data table 3) Find  2 critical 4) Calculate the expected frequencies 5) Calculate  2 6) Decision 7) Put answer into words

3. Example With whom do you find it easiest to make friends? Subjects were either male and female. Possible responses were: “opposite sex”, “same sex”, or “no difference” Is there a significant (.05) relationship between the gender of the subject and their response?

4. Results

5. Step 1: State the Hypothesis H 1: There is a relationship between gender and with whom a person finds it easiest to make friends H 0 :Gender and with whom a person finds it easiest to make friends are independent of each other

6. Step 2: Create the Data Table Add “total” columns and rows

7. Step 3: Find  2 critical df = (R - 1)(C - 1) df = (2 - 1)(3 - 1) = 2  =.05  2 critical = 5.99

8. Step 4: Calculate the Expected Frequencies

9. Step 5: Calculate  2 O = observed frequency E = expected frequency

10. 22

11. 22

12. 22

13. 22

14. 22 8.5

15. Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0

16. Step 6: Decision Thus, if  2 > than  2 criticalThus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0  2 = 8.5  2 crit = 5.99

17. Step 7: Put answer into words H 1: There is a relationship between gender and with whom a person finds it easiest to make friends A persons gender is significantly (.05) related with whom it is easiest to make friends.

18. Practice Is there a significant (  =.01) relationship between opinions about the death penalty and opinions about the legalization of marijuana? 933 Subjects responded yes or no to: “Do you favor the death penalty for persons convicted of murder?” “Do you think the use of marijuana should be made legal?”

19. Results Marijuana ? Death Penalty ?

20. Step 1: State the Hypothesis H 1: There is a relationship between opinions about the death penalty and the legalization of marijuana H 0 :Opinions about the death penalty and the legalization of marijuana are independent of each other

21. Step 2: Create the Data Table Marijuana ? Death Penalty ?

22. Step 3: Find  2 critical df = (R - 1)(C - 1) df = (2 - 1)(2 - 1) = 1  =.01  2 critical = 6.64

23. Step 4: Calculate the Expected Frequencies Marijuana ? Death Penalty ?

24. Step 5: Calculate  2

25. Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0

26. Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 criticalIf  2 < or = to  2 critical –Fail to reject H 0  2 = 3.91  2 crit = 6.64

27. Step 7: Put answer into words H 0 :Opinions about the death penalty and the legalization of marijuana are independent of each other A persons opinion about the death penalty is not significantly (.01) related with their opinion about the legalization of marijuana

29. Sam Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants. (Scores on the SCAT range from 1-9 with high scores representing better performance). Was Sam correct? CAT scores 8 hours sleep group (X) 57535339 4 hours sleep group (Y) 81466412

30. Indepdent t-test (2 sample with equal n) t obs =.847 t crit (one tailed) = 1.76 Sam's hypothesis was not confirmed. He did not find a significant difference between those who slept for four hours versus those who slept for eight hours on cognitive test performance.

31. Below grade level At grade levelAdvanced Pre-School866 No Pre-School6159 Algebra Achievement Levels Before making their recommendations, administrators in a large urban district take a random sample of 50 seventh graders and compare the achievement levels of those who attended pre-school and those who did not. If achievement is independent of attending pre-school then the proportions at each level should be equal. Determine if there is an association between attending preschool and algebra achievement.