1. Chi – Square

2. The graph below shows a few samples of chi – square graphs. Notice when the d.f. increase, the graph will flatten out and the high point ( mode ) shifts right and begins to look more bell shaped.

3. Chi – Square

5. The value we will be looking for is the area in the tail to the RIGHT of the critical value

6. Chi – Square Here is a table of chi square values…

7. Chi – Square Here is a table of chi square values… The left side is degrees of freedom

8. Chi – Square Here is a table of chi square values… The left side is degrees of freedom The top row is area of the right tail

9. Chi – Square Here is a table of chi square values… The left side is degrees of freedom The top row is area of the right tail These values are the probabilities

10. Chi – Square Let’s dive right into an example to learn this… A computer keyboard company has developed two new letter arrangement keyboards. The company wants to see is there any relationship between the arrangement of letters on the keyboard and the number of hours it takes for a new user to be able to type at 20 words per minute.

11. Chi – Square

13. Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total A 25302580 B 307119120 Standard 354916100 Column Total 9015060 300 Sample size This table is called a contingency table. The pink shaded boxes are called cells. These contain the observed frequencies. The size of the contingency table is determined by the number of rows and columns that contain data. This table is a 3 X 3 ( read three by three ) table and contains 9 cells. The row and column totals are not included in the cell count.

14. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total A O = 25 E = ___ O = 30 E = ___ O = 25 E = ___ 80 B O = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 Standard O = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size To use this table correctly, we need to modify it just a bit to show what are called observed and expected frequencies for each cell. The observed frequencies we already knew, it was the sample data.

15. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = ___ O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

16. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = ___ O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

17. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = ___ O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

18. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = ___ O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

19. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = ___ O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

20. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = ___ O = 16 E = ___ 100 Column Total 9015060 300 Sample size

21. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = ___ 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total 9015060 300 Sample size

22. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = 16 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = ___ 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total 9015060 300 Sample size

23. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = 16 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = 24 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = ___ 100 Column Total 9015060 300 Sample size

24. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = 16 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = 24 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = 20 100 Column Total 9015060 300 Sample size

25. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = 16 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = 24 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = 20 100 Column Total 9015060 300 Sample size

26. Chi – Square Keyboard 21 – 40 h41 – 60 h61 – 80 hRow Total AO = 25 E = 24 O = 30 E = 40 O = 25 E = 16 80 BO = 30 E = 36 O = 71 E = 60 O = 19 E = 24 120 StandardO = 35 E = 30 O = 49 E = 50 O = 16 E = 20 100 Column Total 9015060 300 Sample size

27. Chi – Square Cell 12524 23040 32516 43036 57160 61924 73530 84950 91620 So I just transferred the data from my contingency table into this table…

28. Chi – Square Cell 125241 23040-10 325169 43036-6 5716011 61924-5 735305 84950 91620-4

29. Chi – Square Cell 1252411 23040-10100 32516981 43036-636 5716011121 61924-525 73530525 849501 91620-416

30. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80

31. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80 ∑ = 13.31

32. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80 ∑ = 13.31

33. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80 ∑ = 13.31

34. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80 ∑ = 13.31

35. Chi – Square Cell 12524110.04 23040-101002.50 325169815.06 43036-6361.00 57160111212.02 61924-5251.04 735305250.83 8495010.02 91620-4160.80 ∑ = 13.31

36. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

37. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

38. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size 1. State the null and alternate hypotheses

39. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

40. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = O = 57 E = 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

41. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = 54 90 Mountain Mist O = 30 E = O = 20 E = 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

42. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = 54 90 Mountain Mist O = 30 E = 20 O = 20 E = 30 50 Jungle Grape O = 5 E = O = 35 E = 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

43. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = 54 90 Mountain Mist O = 30 E = 20 O = 20 E = 30 50 Jungle Grape O = 5 E = 16 O = 35 E = 24 40 Diet Pop O = 12 E = O = 8 E =20 Column Total 80120 200 Sample size

44. Chi – Square Soda PopHigh School Elementary School Row Total Kula Kola O = 33 E = 36 O = 57 E = 54 90 Mountain Mist O = 30 E = 20 O = 20 E = 30 50 Jungle Grape O = 5 E = 16 O = 35 E = 24 40 Diet Pop O = 12 E = 8 O = 8 E = 1220 Column Total 80120 200 Sample size

45. Chi – Square Cell 13336 25754 33020 4 30 5516 63524 7128 88 ∑ =

46. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ =

47. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ = 24.68

48. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ = 24.68

49. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ = 24.68

50. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ = 24.68

51. Chi – Square Cell 13336-390.25 25754390.17 33020101005.00 42030-101003.33 5516-111217.56 63524111215.04 71284162.00 8812-4161.33 ∑ = 24.68