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.
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.
Ha: 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 = ∑(Oij – Eij)2/Eij
i)
Southeast
Chi Square = ∑(Oij – Eij)2/Eij = (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 = ∑(Oij – Eij)2/Eij = 36.93
Result
Since, Chi Square> Chi Square Critical we reject the null hypothesis.
Conclusion:
Region and Sales are associated.
iii)
Midwest
Chi Square = ∑(Oij – Eij)2/Eij = 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 = ∑(Oij – Eij)2/Eij = 30.5
Result
Since, Chi Square> Chi Square Critical we reject the null hypothesis.
Conclusion:
Region and Sales are associated.
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