Question

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

a)

Hypothesis testing is used to explore the relationship between two or more variables in an experimental setting. Business managers use the results of a hypothesis test when making management decisions. Hypothesis testing allows managers to examine causes and effects before making a crucial management decision.

Eg:

1. if a company is considering offering flexible work hours to your employees, they might hypothesize that this policy change will positively affect their productivity.
2. A small business might want to test the cost of acquiring a customer. Hypothesizing this value guides not only on their pricing strategy but also marketing efforts and managing other expenses

b)

Chi Square = ?(O_ij – E_ij)²/E_ij

Where, O_ij is the observed value and E_ij is the expected value.

Hence,

Southeast

Chi Square = (98-100)²/100 + (104-100)²/100 = 0.2

Northeast

Chi Square = (188-150)²/150 + (214-150)²/150 = 36.93

Midwest

Chi Square = (120-125)²/125 + (108-125)²/125 = 2.512

Pacific

Chi Square = (205-200)²/200 + (278-200)²/200 = 30.545

c)

Alpha = 0.05

Assuming there are 2 groups for each region

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

Chi Square Critical = 3.84

Decision Rule:

If Chi Square > Chi Square _Critical reject the null hypothesis

Hence,

Southeast

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

Northeast

Since, Chi Square > Chi Square _Critical reject the null hypothesis in favour of Alternate Hypothesis

Midwest

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

Pacific

Since, Chi Square > Chi Square _Critical reject the null hypothesis in favour of Alternate Hypothesis.

d)

The company should also consider doing the correlation test between the two variables to check for association.

e)

chi-square test of independence can be used to verify the influence of gender on purchase decisions. Are men the primary decision makers when it comes to purchasing a big ticket items? Is gender a factor in color preference of a car? Here variable X would be gender and variable Y would be color.