2. 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?”

3. Results Marijuana ? Death Penalty ?

4. 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

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

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

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

8. Step 5: Calculate  2

9. 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

10. 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

11. 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

13.  2 as a test for goodness of fit So far.... The expected frequencies that we have calculated come from the data They test rather or not two variables are related

14.  2 as a test for goodness of fit But what if: You have a theory or hypothesis that the frequencies should occur in a particular manner?

15. Example M&Ms claim that of their candies: 30% are brown 20% are red 20% are yellow 10% are blue 10% are orange 10% are green

16. Example Based on genetic theory you hypothesize that in the population: 45% have brown eyes 35% have blue eyes 20% have another eye color

17. To solve you use the same basic steps as before (slightly different order) 1) State the hypothesis 2) Find  2 critical 3) Create data table 4) Calculate the expected frequencies 5) Calculate  2 6) Decision 7) Put answer into words

18. Example M&Ms claim that of their candies: 30% are brown 20% are red 20% are yellow 10% are blue 10% are orange 10% are green

19. Example Four 1-pound bags of plain M&Ms are purchased Each M&Ms is counted and categorized according to its color Question: Is M&Ms “theory” about the colors of M&Ms correct?

21. Step 1: State the Hypothesis H 0 : The data do fit the model –i.e., the observed data does agree with M&M’s theory H 1: The data do not fit the model –i.e., the observed data does not agree with M&M’s theory –NOTE: These are backwards from what you have done before

22. Step 2: Find  2 critical df = number of categories - 1

23. Step 2: Find  2 critical df = number of categories - 1 df = 6 - 1 = 5  =.05  2 critical = 11.07

24. Step 3: Create the data table

25. Add the expected proportion of each category

26. Step 4: Calculate the Expected Frequencies

27. Expected Frequency = (proportion)(N)

28. Step 4: Calculate the Expected Frequencies Expected Frequency = (.30)(2081) = 624.30

29. Step 4: Calculate the Expected Frequencies Expected Frequency = (.20)(2081) = 416.20

30. Step 4: Calculate the Expected Frequencies Expected Frequency = (.20)(2081) = 416.20

31. Step 4: Calculate the Expected Frequencies Expected Frequency = (.10)(2081) = 208.10

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

33. 22

34. 22

35. 22

36. 22

37. 22

38. 22 15.52

39. 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

40. 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 = 15.52  2 crit = 11.07

41. Step 7: Put answer into words H 1: The data do not fit the model M&M’s color “theory” did not significantly (.05) fit the data

43. Practice Among women in the general population under the age of 40: 60% are married 23% are single 4% are separated 12% are divorced 1% are widowed

44. Practice You sample 200 female executives under the age of 40 Question: Is marital status distributed the same way in the population of female executives as in the general population (  =.05)?

46. Step 1: State the Hypothesis H 0 : The data do fit the model –i.e., marital status is distributed the same way in the population of female executives as in the general population H 1: The data do not fit the model –i.e., marital status is not distributed the same way in the population of female executives as in the general population

47. Step 2: Find  2 critical df = number of categories - 1

48. Step 2: Find  2 critical df = number of categories - 1 df = 5 - 1 = 4  =.05  2 critical = 9.49

49. Step 3: Create the data table

50. Step 4: Calculate the Expected Frequencies

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

52. 22 19.42

53. 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

54. 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 = 19.42  2 crit = 9.49

55. Step 7: Put answer into words H 1: The data do not fit the model Marital status is not distributed the same way in the population of female executives as in the general population (  =.05)

57. Practice Is there a significant (  =.05) relationship between gender and a persons favorite Thanksgiving “side” dish? Each participant reported his or her most favorite dish.

58. Results Side Dish Gender

59. Step 1: State the Hypothesis H 1: There is a relationship between gender and favorite side dish Gender and favorite side dish are independent of each other

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

61. Results Side Dish Gender

62. Step 5: Calculate  2

63. 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

64. 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 = 13.15  2 crit = 5.99

65. Step 7: Put answer into words H 1: There is a relationship between gender and favorite side dish A person’s favorite Thanksgiving side dish is significantly (.05) related to their gender

67. Practice 13.7 For each example (i, ii, iii, iv) make LINE Graphs and determine if: –1) Any main effects? –2) Any interaction effects?

68. Practice Age: No Games: NO Interaction: YES

69. Practice Age: No Games: NO Interaction: YES

70. Practice Dose: Yes Diagnosis: Yes Interaction: No

71. Practice Dose: Yes Diagnosis: Yes Interaction: No

72. Practice Height: Yes Grade: Yes Interaction: Yes

73. Practice Height: Yes Grade: Yes Interaction: Yes

74. Practice Gender: NO SES: Yes Interaction: Yes (very small)

75. Practice Gender: NO SES: Yes Interaction: Yes (very small)

77. 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

78. 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.

79. Cookbook