1. A company listed five categories and asked each employee to mark the one most important to him or her. The company wants to determine if the current distribution of responses “fits” last year’s distribution or is it different. When considering questions of this type, we are asking whether a population follows a specified distribution.

5. Here is the table of last year’s responses…

6. The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30 Salary 290 Safety Regulations 70 Health & Retirement Benefits 70 Overtime Policy & Pay 40

7. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30 Salary 290 Safety Regulations 70 Health & Retirement Benefits 70 Overtime Policy & Pay 40 To find the expected frequencies, we will multiply each % favorable from the previous population by 500…

8. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290 Safety Regulations 70 Health & Retirement Benefits 70 Overtime Policy & Pay 40 4% X 500 = 0.04 X 500 = 20

9. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290325 Safety Regulations 70 Health & Retirement Benefits 70 Overtime Policy & Pay 40 4% X 500 = 0.04 X 500 = 20 65% X 500 = 0.65 X 500 = 325

10. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290325 Safety Regulations 7065 Health & Retirement Benefits 70 Overtime Policy & Pay 40 4% X 500 = 0.04 X 500 = 20 65% X 500 = 0.65 X 500 = 325 13% X 500 = 0.13 X 500 = 65

11. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290325 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 40 4% X 500 = 0.04 X 500 = 20 65% X 500 = 0.65 X 500 = 325 13% X 500 = 0.13 X 500 = 65 12% X 500 = 0.12 X 500 = 60

12. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290325 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030 4% X 500 = 0.04 X 500 = 20 65% X 500 = 0.65 X 500 = 325 13% X 500 = 0.13 X 500 = 65 12% X 500 = 0.12 X 500 = 60 6% X 500 = 0.06 X 500 = 30

13. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020 Salary 290325 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030

14. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 290325 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030

15. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 2903251225 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030

16. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 2903251225 Safety Regulations 706525 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030

17. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 2903251225 Safety Regulations 706525 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030

18. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 2903251225 Safety Regulations 706525 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030100

19. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 3020100 Salary 2903251225 Safety Regulations 706525 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030100

20. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30201005.00 Salary 2903251225 Safety Regulations 706525 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030100 100/20 = 5

21. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 706525 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030100 1225/325 = 3.77

22. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 7060100 Overtime Policy & Pay 4030100 25/65 = 0.38

23. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 4030100 100/60 = 1.67

24. Here is the table of last year’s responses… The new year’s responses were drawn from a sample of 500 employees. We need to set up the chi – square computation table… Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 40301003.33 100/30 = 3.33

25. Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 40301003.33 ∑ = 14.15 Now sum that column…

26. Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 40301003.33 ∑ = 14.15 Now sum that column…

27. Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 40301003.33 ∑ = 14.15 Now sum that column…

28. Category Vacation Time 30201005.00 Salary 29032512253.77 Safety Regulations 7065250.38 Health & Retirement Benefits 70601001.67 Overtime Policy & Pay 40301003.33 ∑ = 14.15 Now sum that column…

29. So we are basically doing the chi – square steps. The only difference is our expected outcomes are based on a previous population’s random sample. Let’s try another example…

30. EXAMPLE # 2 : The age of distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below. Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Age ( years )% Canadian Pop. Observed Number in Red Lake Village Under 57.2%47 5 to 1413.6%75 15 to 6467.1%288 65 and older12.1%45

31. EXAMPLE # 2 : The age of distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below. Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Age ( years )% Canadian Pop. Observed Number in Red Lake Village Under 57.2%47 5 to 1413.6%75 15 to 6467.1%288 65 and older12.1%45 Age Under 547 5 – 1475 15 – 65288 65 or older45 ∑ = Set up your chi – square computation table and fill in the observed frequencies and the rest of the cells…

32. EXAMPLE # 2 : The age of distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below. Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Age ( years )% Canadian Pop. Observed Number in Red Lake Village Under 57.2%47 5 to 1413.6%75 15 to 6467.1%288 65 and older12.1%45 Age Under 54733 5 – 147562 15 – 65288305 65 or older4555 ∑ = 455 X 0.072 = 33 455 X 0.136 = 62 455 X 0.671 = 305 455 X 0.121 = 55

33. EXAMPLE # 2 : The age of distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below. Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Age ( years )% Canadian Pop. Observed Number in Red Lake Village Under 57.2%47 5 to 1413.6%75 15 to 6467.1%288 65 and older12.1%45 Age Under 54733196 5 – 147562169 15 – 65288305289 65 or older4555100 ∑ =

34. EXAMPLE # 2 : The age of distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below. Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Age ( years )% Canadian Pop. Observed Number in Red Lake Village Under 57.2%47 5 to 1413.6%75 15 to 6467.1%288 65 and older12.1%45 Age Under 547331965.94 5 – 1475621692.73 15 – 652883052890.95 65 or older45551001.82 ∑ = 11.44

35. Age Under 547331965.94 5 – 1475621692.73 15 – 652883052890.95 65 or older45551001.82 ∑ = 11.44

36. Age Under 547331965.94 5 – 1475621692.73 15 – 652883052890.95 65 or older45551001.82 ∑ = 11.44

37. Age Under 547331965.94 5 – 1475621692.73 15 – 652883052890.95 65 or older45551001.82 ∑ = 11.44