University Financial Statistics Homework: Household Data Analysis

This financial statistics assignment analyzes a dataset of 250 households, examining expenditures on alcohol, meals, fuel, and phone, alongside income data. The assignment begins with descriptive statistics, including mean, standard deviation, and box-whisker plots, revealing the distribution of expenditures and their skewness. It then delves into income analysis, comparing the top and bottom 10% of earners, and calculates the proportion of households owning a house. Regression analysis is performed to explore the relationship between total expenditures and after-tax income, determining the correlation coefficient. Finally, the assignment investigates the relationship between gender, education level, and their probabilities, including the determination of independence between these variables. The analysis employs techniques such as contingency tables and probability calculations to derive meaningful insights from the household data.

Running head: FINANCIAL STATISTICS
Financial Statistics
Name of the Student:
Name of the University:
Author note:

1FINANCIAL STATISTICS
Table of Contents
Task 1...............................................................................................................................................2
Part a............................................................................................................................................2
Part b............................................................................................................................................2
Part c............................................................................................................................................3
Task 2...............................................................................................................................................4
Part a............................................................................................................................................4
Part b............................................................................................................................................4
Part c............................................................................................................................................5
Task 3...............................................................................................................................................6
Part a............................................................................................................................................6
Part b............................................................................................................................................6
Part c............................................................................................................................................7
Part d............................................................................................................................................7
Part e............................................................................................................................................7
References........................................................................................................................................9

2FINANCIAL STATISTICS
Task 1
Part a
The random sample of two hundred and fifty (250) households as per the Sample
Selection Procedure is drawn using simple random sampling technique by applying Random
function in MS Excel. This technique of simple random sampling is the most suitable method as
the overall population will be studied and not any particular group. Furthermore, simple random
sampling reduces sampling biasness and thereby generates more unbiased outcomes (Lohr 2019).
Part b
Descriptive
Statistics Alcohol Meals Fuel Phone
Mean 1136.41 1318.18 1971.65 1466.86
Standard Error 91.02 203.51 116.91 82.96
Median 652 870 1440 1200
Mode 0 0 2400 1200
Standard
Deviation 1439.17 3217.73 1848.54 1311.63
Sample Variance
2071196.
64
10353773.
91
3417106.
64
1720385.
40
Kurtosis 18.28 179.48 7.78 5.97
Skewness 2.99 12.49 2.24 2.17
Range 13035 48000 12000 8400
Minimum 0 0 0 0
Maximum 13035 48000 12000 8400
Sum 284102 329544 492912 366714
Count 250 250 250 250
Table 1: Descriptive statistics for expenditures on alcohol, meals, fuel and phone

3FINANCIAL STATISTICS
The descriptive statistics for the expenditures on the variables Alcohol, Meals, Fuel and Phone
are described in the above table. It is found that the average expenditure is highest for Fuel
($1971.65) and lowest for Alcohol ($1136.41). The minimum expenditure for all the four
variables is $0 while the maximum expenditure occurs for meals ($48000).
Alcohol Meals Fuel Phone
-500
9500
19500
29500
39500
49500
Expenditures
Figure 1: Box-Whisker plot of Expenditures
The Box-Whisker plot of Expenditures shows that the distribution of the expenditures for all the
variables is skewed to the right. This implies that the means of all the four variables are more
than their median values and this can be seen from Table 1. The median expenditure is highest
for Fuels ($1440).
Part c
From the above table on descriptive statistics and figure of box-plot, it is observed that
the household expenditure on the variables, Alcohol, Meals, Fuels and Phone, is skewed to the
right, which implies that the mean or average expenditures on these four variables are higher
than their median expenditures. The descriptive statistics shows that the median expenditure is

4FINANCIAL STATISTICS
lowest for alcohol and highest for fuels. Moreover, there is a significant variation among the
expenditures on these four variables.
Task 2
Part a
Average income Maximum income
value
Minimum income
value
Top 10% $155540.8 $418490 $103916
Bottom 10% $13660.2 $18484 $6590
The average of top 10% value of the household’s annual after tax income is $155540.8 and thus,
10% of the households from the sample of 250 have annual income after tax of more than
$103916.
The average of bottom 10% value of the household’s annual after tax income is $13660.2 and
these bottom 10% of the households have annual income after tax less than $18484.
Part b
The number of households in the sample that owns a house is 184 and otherwise is 66.
OWNhouse Count
Owns a house 184
Otherwise 66
The proportion of households that owns a house in the sample = 184
250 = 0.736

5FINANCIAL STATISTICS
The combination of any 3 out of 5 randomly chosen households with a house = cr
n = c3
5 = 10
Required Probability = [10 * (0.74^5) * (1-0.74)^2] = 0.15
Part c
8 10 12 14
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
f(x) = 0.446814676918168 x + 5.15532442119845
R² = 0.36359257401864
ln(Texp)
Figure 2: Scatter plot of ln(Texp) against ln(AtaxInc)
The coefficient of correlation between ln(Texp) and ln(Ataxinc) is:
ln(ATaxInc) ln(Texp)
ln(ATaxInc
)
1
ln(Texp) 0.602986 1

6FINANCIAL STATISTICS
The above scatter plot between ln(Texp) and ln(Ataxinc) shows that there is a linear relationship
between the natural logarithms of the total expenditures and the after tax income. The value of
correlation coefficient is 0.642. Hence, there is a positive and moderate linear relationship
between the variables.
Task 3
Part a
The contingency table between the gender and the level of education is shown in the excel sheet
attached herewith.
Row Labels Bachelor
Intermediat
e Master Primary
Secondar
y Grand Total
Female 34 19 18 22 29 122
Male 20 32 32 21 23 128
Grand Total 54 51 50 43 52 250
Table 2: Count of Gender with Highest Degree
Highest degree
Gender Bachelo
r
Intermediate Master
s
Primary Secondary Grand
Total
Female 0.136 0.076 0.072 0.088 0.116 0.488
Male 0.08 0.128 0.128 0.084 0.092 0.512
Table 3: Proportion of Gender and Highest Degree

7FINANCIAL STATISTICS
From the above two tables, the proportion of females and males are found and it is seen that the
proportions are different.
Part b
The number of male heads with Masters as their highest degree = 32
The number of households counted = 250
Thus, the probability that the head of household is a male and his higher level of
education is Masters ¿ 32
250 =0.12 8
Part c
The number of male heads with Masters as their highest degree = 32
The number of males = 128
Thus, the probability that the head of household is a male and his higher level of education is
Bachelor ¿ 32
128 =0.25
Part d
The number of female heads with Bachelor as their highest degree = 34
The number of households with female heads = 122
Thus, the probability that the head of household is a female and her higher level of education is
Bachelors ¿ 34
122=0.279

8FINANCIAL STATISTICS
Part e
The events "gender of household head is female" and "Primary as higher level of education" are
independent, if,
P(gender of household head is female) x P(having the Primary Degree) = P(household head is
female and has Primary degree)
Number of households with female heads = 122
Thus, P(gender of household head is female) = 122
250 =0. 488
Number of households with Primary as highest degree = 43
Thus, P(having the Primary Degree) ¿ 43
25 0 =0.172
Number of household female heads with Primary as highest degree = 22
The, P(household head is female and has Primary degree) = 22
250 =0.0 88
Hence, P ( gender of household head is fe male ) x P ( having the Primary Degree )=0.488 x 0. 172
= 0.083
Since, P(gender of household head is female) x P(having the Primary Degree) ≠ P(household
head is female and has primary degree), hence they are not independent.

9FINANCIAL STATISTICS
References
Lohr, S.L., 2019. Sampling: Design and Analysis: Design and Analysis. Chapman and
Hall/CRC.