ETS2111 Business Data Modelling Assignment 2022

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ETS2111 Business Data Modelling Assignment
Question 1
a) Gender is a categorical variable whose measurement scale (Male and Female) is the
ordinal scale. Similarly, ‘Buy Category' is a categorical variable with ordinal
measurement scale (High, Medium and Low)
b) Table 1 provides frequency counts for cells created based on categories of variables
‘Gender' and ‘Buy Category'
Buy-Category
Gender High Low Medium
Grand
Total
Female 69 79 56 204
Male 39 61 46 146
Grand Total 108 140 102 350
Table 1: A contingency Table of Gender vs. Buy-Category counts
c) To test whether purchasing behavior is related to the gender of the customer, we use
the Chi-Square test for independence or association. Assuming that the test statistic is
Q,
Q Xk
2
Where k is a positiveinteger indicating the degrees of freedom .
For a Chi-Square test of association, the degrees of freedom (DF) is given by:
DF (k)= ( r−1 )∗( c−1)
Where c∧r arethe levels of each categorical variable .
Therefore, From Table 1,
k = ( 2−1 )∗( 3−1 ) =2
Thus
Q X2
2

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d) To test whether purchasing behavior is related to the gender of the customer, the first
step involves stating the null and alternative hypothesis:
H0 :Gender∧Purchasing Behaviour are independent
Ha :Gender∧Purchasing behavior are not independent
Next, the Chi-Square test statistic is determined.
χ2= ( Observed Value−Expected Value )2
Expected Value
Each expected value is determined by multiplying each row total by each column total
and dividing by the overall total. Therefore, using Table 1, the following table of
expected frequencies is generated:
Expected Frequencies
Buy-Category
Gender High Low Medium Total
Female 62.9486 81.6000 59.45142857 204
Male 45.0514 58.4000 42.54857143 146
Total 108 140 102 350
Table 2: Table of Expected Frequencies
Using Table 2 Values and Chi-Square Formula, a table of Chi-Square values is generated:
Chi-Square Values
0.5817 0.0828 0.2004
0.8128 0.1158 0.2800
Table 3: Chi-Square values (Test statistic)
Therefore, Chi-Square test statistic,
¿ 0.5817+ 0.0828+ 0.2004+0.8128+ 0.1158+0.28=2.0735
Using CHIINV function in excel at DF=2 and 1% level of significance, the critical value is
9.2103. Given that the test statistic is less than the critical value, we fail to reject the null

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hypothesis and conclude that there is significant statistical evidence to indicate that gender
and purchasing behavior is independent.
Question 2
a) ANOVA test could be used to compare the mean ages of workers at the four
locations. The types of variations that could be used include unidirectional (one-way)
and multidirectional (two-way) variations. In this case, one-way ANOVA is
appropriate because only one independent variable being considered. An ANOVA
test, it is assumed that the test statistic (response variable residuals) follows a normal
distribution. In a one-way ANOVA test, the test statistic depends on a set of three
degrees of freedom: Between the Groups DF, Within the Groups DF and Total DF.
BetweenGroups DF=k−1 ; where k isthe total number of groups . Therefore ,
BetweenGroups DF=4−1=3
WithinGroups DF=N −k ; where N is the total number of observations. Thus ,
WithinGroups DF=24−4=20
Total DF =N−1=24−1=23
b) The null and alternative hypotheses in this case are:
H0 : μA =μB =μC=μ❑
Ha : μi ≠ μm
Where μi∧μm arethe means of any of the two samples ,∧μA ... μD are the means of
sample A ¿ D
Table 4 below summarizes the output of One-Way ANOVA test in Excel:
One-Way ANOVA
SUMMARY
Groups Count
Su
m
Averag
e
Varianc
e