Question

Quantitative Methods and Analysis Course

One of the items that businesses would like to be able to test is whether or not a change they make to their procedures is effective. Remember that when you create a hypothesis and then test it, you have to take into consideration that some variance between what you expect and what you collect as actual data is because of random chance. However, if the difference between what you expect and what you collect is large enough, you can more readily say that the variance is at least in part because of some other thing that you have done, such as a change in procedure.
For this submission, you will watch a video about the Chi-square test. This test looks for variations between expected and actual data and applies a relatively simple mathematical calculation to determine whether you are looking at random chance or if the variance can be attributed to a variable that you are testing for.
Imagine that a company wants to test whether it is a better idea to assign each sales representative to a defined territory or allow him or her to work without a defined territory. The company expects their sales reps to sell the same number of widgets each month, no matter where they work. The company creates a null and alternate hypothesis to test sales from defined territory sales versus open sales.
One of the best ways to test a hypothesis is through a Chi-square test of a null hypothesis. A null hypothesis looks for there to be no relationship between two items. Therefore, the company creates the following null hypothesis to test: There is no relationship between the amount of sales that a representative makes and the type of territory (defined or open) that a representative works in. The alternate hypothesis would be the following: There is a relationship between the kind of sales territory a sale representative has (defined or open) and the amount of sales he or she makes during a month.

Step 1:
Watch this video. Bozeman Chi-squared Test on YouTube

Step 2:
Use the following data to conduct a Chi-square test for each region of the company in the same manner you viewed in the video:

Region
                             Expected                   Actual
Southeast

Defined                 100                                  98
            
Open                    100                              104
          
Northeast

Defined                 150                                188

Open                     150                                214

Midwest

Defined                 125                                120

Open                     125                                108

Pacific

Defined                 200                               205

Open                    200                                278

Step 3:
Write an 800–1,000-word essay, utilizing APA formatting, to discuss the following:
• Describe why hypothesis testing is important to businesses.
• Report your findings from each Chi-square test that you conducted.
• Based solely on the Chi-square test, discuss whether the company should accept the null hypothesis in each region or reject it in favor of the alternate hypothesis.
• Discuss any other statistical analyses you would want the company to contemplate before deciding if it will go with a defined or open sales strategy.
• Describe and discuss at least 1 other business scenario in which you believe Chi-square testing would be helpful to a company.

Answer 1

Soln

a)

Hypothesis testing explores the effect of one factor on another by exploring the relationship's statistical significance. For example, a hypothesis test may be set up in order to explain how much an increase in labor affects productivity.

b)

H₀: The two variables (Region and Sales) are independent.

H_a: The two variables are associated.

alpha = 0.05

df = (r-1)*(c-1) = (2-1)*(2-1) = 1*1 = 2

Chi Square _Critical = 3.84

Decision Rule:

If Chi Square> Chi Square _Critical reject the null hypothesis

Test Statistic:

Chi Square = ∑(O_ij – E_ij)²/E_ij

i)

Southeast

Chi Square = ∑(O_ij – E_ij)²/E_ij = (98-100)²/100 + (104 – 100)²/100 = 0.2

Result

Since, Chi Square< Chi Square _Critical fail to reject the null hypothesis.

Conclusion:

Region and Sales are independent.

ii)

Northeast

Chi Square = ∑(O_ij – E_ij)²/E_ij = 36.93

Result

Since, Chi Square> Chi Square _Critical we reject the null hypothesis.

Conclusion:

Region and Sales are associated.

iii)

Midwest

Chi Square = ∑(O_ij – E_ij)²/E_ij = 1.4

Result

Since, Chi Square< Chi Square _Critical fail to reject the null hypothesis.

Conclusion:

Region and Sales are independent.

iv)

Pacific

Chi Square = ∑(O_ij – E_ij)²/E_ij = 30.5

Result

Since, Chi Square> Chi Square _Critical we reject the null hypothesis.

Conclusion:

Region and Sales are associated.