University Statistics: Household Analysis Assignment, Semester 1

This document presents a complete solution to a household analysis assignment, likely for a statistics or data analysis course. The assignment covers several key areas, including random sampling techniques, data visualization (likely through charts), and statistical analysis. Task 1 focuses on data acquisition using random sampling, followed by the analysis of expenditure data, possibly using box plots or other visual representations to highlight spending patterns across different categories (alcohol, meals, fuel, phone). Task 2 delves into the analysis of utility expenditure using a cumulative frequency graph to determine the proportion of households spending within certain annual ranges. Task 3 explores confidence intervals for after-tax income and applies probability concepts to household characteristics, such as house ownership. Finally, Task 4 involves creating a contingency table to analyze the relationship between gender and education level and calculating probabilities based on the data presented, including conditional probabilities and tests for independence.

RUNNING HEADER: HOUSEHOLD ANALYSIS 1
Household analysis
Students’ name:
Student’s ID:
Institution:

Household analysis 2
TASK 1
A. A random sampling technique was used to acquire data. The technique was chosen so as to get
data that is a non-biased representation of the total population.
B. Plot
Alcohol Meals Fuel Phone
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Expenditure
C. Findings
It can be seen that the highest expenditure is spent on fuel while the lowest expenditure is spent on
alcohol. Fuel has the highest interquartile range comparted to alcohol, meals and phone while meals has
the lowest interquartile range. Fuel also has the highest median expenditure than the other three items.
The results therefore suggest that the highest expenditure is consistently spent on fuel.
TASK 2
A.

Household analysis 3
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 More
0
10
20
30
40
50
60
Utilities
B.
a. at the most $900 per annum
n (at most $900) = 60
% (at most $900) = 24%
b. between $1500 and $2700 per annum
n (between $1500 and $2700) = 83
% (between $1500 and $2700) = 33%
c. more than $3000 per annum
n (more than $3000) = 12
% (more than $3000) = 5%
TASK 3
A.
The bottom 5% value is $12,220 while the top 5% value is $135,938.
Thus, the 95% confidence range of getting the after tax income is between $12,220 and $135,938.

Household analysis 4
B.
(i) X will be a quantitative variable since it represents the number of households who own a
house.
(ii) The probability of only 1 household owning a house is 50%. 1 household has 2 options to
own a house or not. Thus, ½ = 50%.
The probability if X is 250 is 75%. 187 households own a house while 63 people do not. Thus,
187/250 = 75%.
Scatter plot
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
0
2
4
6
8
10
12
14
Coefficient of correlation = 0.614
From the coefficient of correlation, it is evident that there is a strong and positive relationship between
total expenditure and after-tax income.
Task 4
A.
Row Labels B I M P S Grand Total
F 21 18 25 31 29 124
M 20 24 28 28 26 126
Grand Total 41 42 53 59 55 250

Household analysis 5
B.
P (male and intermediate) = n (male and intermediate) / n (intermediate)
P = 24 / 42 = 0.57
C.
P (female and bachelor) = n (female and bachelor) / n (bachelor)
P = 21 / 41 = 0.51
D.
Proportion = males (masters) / total males
Proportion = 28 / 126 = 0.22
E.
P (female) = n (female) / n (grand total)
P (female) = 124 / 250
P (masters) = n (masters) / n (grand total)
P (masters) = 53 / 250
P (female and masters) = n (female and masters) / n (grand total)

Household analysis 6
P (female and masters) = 25 / 250
= 124 / 250 * 53 / 250 ≠ 25 / 250
Thus, the “gender of household is female” and “having the Master Degree” are dependent events.