Business Data Modelling - Desklib

Running head: STATISTICS 1
Business Data Modelling
Student Name
Professor’s Name
University Name
Date

STATISTICS 2
Business Data Modelling
Question 1: Analysis of Elect-Mart Company Data
a. Description of Variables
The variable gender is a categorical/qualitative variable with nominal level of
measurement. On the other hand, the variable Buyer Category is a
categorical/qualitative data with ordinal level of measurement.
b. Pivot Table
The pivot table that provides frequency counts for cells created on the basis of variables
gender and buy category is shown below:
c. Testing for independence
To test whether purchasing behavior of customer is related to gender we use the Chi
square test for independence. The test statistic follows the Pearson’s Chi Square
Distribution. The degrees of freedom are given:
df =(R−1)( C−1)
df = ( 3−1 ) ( 2−1 )
df =2
d. Critical Value Approach to Test for Independence.
The null and the alternative hypothesis are stated as follows:
Null hypothesis Ho :Gender∧Buying Category areindependent
Alternative hypothesis H1 :Gender∧Buying category are not independent

STATISTICS 3
The test statistic is given by:
X2 =∑ (O−E)2
E
Where O is the frequency observed, and E the frequency that is expected.
The observed frequencies are shown below:
The expected frequencies are given by:
E= Row total∗column total
N
The are summarized in the table below.
Expected Frequecies
Row High Low Medium Total
Female 62.95 81.60 59.45 204.00
Male 45.05 58.40 42.55 146.00
Total 108.00 140.00 102.00 350.00
The Test Statistics is given by:
X2 =(69.0−62.95)2
62.95 + (79−81.6)2
81.6 + (56−59.45)2
59.45 + (39−45.05)2
45.05 + (61−58.40)2
58.40 + ( 46−42.55)2
42.55
X2 =0.58+0.08+0.20+ 0.81+ 0.12+0.28
X2 =2.07
For 2 degrees of freedom and 0.01 significance level the critical value from the chi-
square table is 9.2104. The decision rule is that we reject the null hypothesis if the test
statistic determined is greater than the critical value. In this case:
Ho : x2 calc< x2 critic

STATISTICS 4
2.07< 9.21
Therefore, we fail to reject the null hypothesis since there is sufficient evidence to prove
that buying category and gender are independent of each other.
Question 2: Hypothesis Test for Mean
a. The methodology that would be used to compare the mean ages of the workers at the four
locations is the analysis of variance. The type of variations that get used in the test are;
Explained variation and Unexplained Variation. The distribution follows the F-test
distribution. The degrees of freedom are given by:
df t =df B +df w
The degrees of freedom between groups is given by the number of groups minus 1:
df B=Ngroups−1
df B=4−1=3
The degrees of freedom within the groups is given by the total number of subjects minus
the number of groups:
df w=N−Ngroups
df w=24−4=20
Total degrees of freedom:
df t =20+3=23 degrees of freedom
b. The null and the alternative hypothesis are stated as below:
The null hypothesis is that there is no difference in the means while the alternative
hypothesis is that at least one of the means is different.
Null hypothesis Ho : μ1=μ2 ¿ μ3 ¿ μ4
Alternative Hypothesis H1 : μ1 ≠ μ2 ≠ μ3 ≠ μ4