Use the following data to conduct a Chi-square test for each region of the compa

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:

Actual

Defined

Open

Defined

Open

Defined

Open

Defined

Open

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.

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

Explanation / Answer

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:

b)

Chi Square = ?(Oij – Eij)2/Eij

Where, Oij is the observed value and Eij 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.

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