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.
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
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…
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
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 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
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 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 = % X 500 = 0.13 X 500 = 65
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 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 = % X 500 = 0.13 X 500 = 65 12% X 500 = 0.12 X 500 = 60
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 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay % X 500 = 0.04 X 500 = 20 65% X 500 = 0.65 X 500 = % X 500 = 0.13 X 500 = 65 12% X 500 = 0.12 X 500 = 60 6% X 500 = 0.06 X 500 = 30
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 Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030
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 Salary Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030
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 Salary Safety Regulations 7065 Health & Retirement Benefits 7060 Overtime Policy & Pay 4030
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 Salary Safety Regulations Health & Retirement Benefits 7060 Overtime Policy & Pay 4030
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay 4030
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay /20 = 5
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay /325 = 3.77
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay /65 = 0.38
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay /60 = 1.67
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 Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay /30 = 3.33
Category Vacation Time Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay ∑ = Now sum that column…
Category Vacation Time Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay ∑ = Now sum that column…
Category Vacation Time Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay ∑ = Now sum that column…
Category Vacation Time Salary Safety Regulations Health & Retirement Benefits Overtime Policy & Pay ∑ = Now sum that column…
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…
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 %75 15 to % and older12.1%45
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 %75 15 to % and older12.1%45 Age Under – – or older45 ∑ = Set up your chi – square computation table and fill in the observed frequencies and the rest of the cells…
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 %75 15 to % and older12.1%45 Age Under – – or older4555 ∑ = 455 X = X = X = X = 55
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 %75 15 to % and older12.1%45 Age Under – – or older ∑ =
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 %75 15 to % and older12.1%45 Age Under – – or older ∑ = 11.44
Age Under – – or older ∑ = 11.44
Age Under – – or older ∑ = 11.44
Age Under – – or older ∑ = 11.44