Analysis of Factors Influencing Pocket Expenses of College Students


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Analysis of Factors Influencing Pocket Expenses of College Students


INTRODUCTION

The area under discussion in the following report is the relationship
between the factors affecting pocket expenses of college students. It
envelops a range of processes and techniques, which were employed to
collect data regarding the above-mentioned theme, as well as a
detailed analysis of the same. Suitable diagrams and graphs have been
included in the report so as to make it interesting and simple for the
reader. Concurrently it puts in numerous tests like f-distribution
test, chi square distribution test, test for goodness of fit, z-test
for correlation and other miscellaneous tests to clarify the subject
matter. In addition it enlightens the Excel functions being used for
the analysis as well as a brief summary and conclusion of the whole
report.


METHODOLOGY

The key word in statistics is 'data'. Data refers is all the
information collected in any form for analysis. Data may be expressly
collected for a specific purpose. Such data are known as primary data.
The collection of facts and figures relating to the population in the
census provides primary data. Often, however data collected for some
purpose, frequently for administrative reasons, may be used. Such data
are known as secondary data. The following methods are generally
adopted for collecting the data.

· Postal questionnaire

· Questionnaires to be filled in by enumerators

· Telephonic interview

· Observation Reports

· Results of experiments

Some other modern techniques used for collecting data are:

· E-mail

· Having questionnaires put up on chat rooms

·

Collection of Data

We followed a planned strategy for the collection of data. As our
topic was concerned with college students we targeted the
universities, cafeterias, call centres, cinemas and other rendezvous
places such as Priya's, DT malls etc. As we were a group of 3 we
divided these places according to locations convenient for each. As it
was time for admissions we knew the target would be the Delhi

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University and there is where we got most of our data. We stood near
the admission office and as students came to collect admission forms
we asked them to spare a minute explaining them the purpose of the
questionnaires. To get a wide array of people we also went to colleges
of fashion designing (NIFD), interior decoration, engineering colleges
and other colleges of vocational studies.

We also e-mailed the questionnaires to our friends staying or studying
abroad in order to see how their expenditure differs from ours. The
questionnaires were mailed to U.S.A, U.K and Australia. We converted
their currency in rupees to have the data in the same currency in
order to make interpretation easier. We also posted the questionnaires
on the yahoo chat room notice board for others to fill in n give their
opinion. As we kept the name as optional most of them filled in as
they knew their identity would be kept secret.


DESCRIPTIVE ANALYSIS

Statistics is a subject, which can be (and is) applied to every aspect
of our lives. The aim of statistical methods is simple: to present
information in a clear, concise and accurate manner. The difficulty in
analysing many phenomena, be they economic, social or otherwise, is
that there is simply too much information for the mind to assimilate.
The task of descriptive methods is therefore to summarize all this
information and draw out the main features, without distorting the
picture. Descriptive statistic uses graphs and statistical formulae in
order to interpret the information and get desired results.

Our research considered various quantitative as well as qualitative
factors that influence the pocket expenses of college students. The
qualitative data was made quantifiable with the help of dummy
variables. Also, factors like the highest level of education of
parents were converted into years of education. All data was clearly
represented in a spreadsheet format in Microsoft Excel, where the
serial number of the entry corresponded to the survey form number on
the questionnaire. Here functions such as 'sort in ascending order'
were used. With the help of this it was evident that the sample space
used was appropriate to comment on the population. [As the monthly
pocket money, 'Y' ranged from Rs.500 to Rs.15000.]

This section on descriptive analysis involves the inferences drawn out
when different variables are linked either individually with the 'Y'
factor or with each other with the help of histograms, pie charts, and
other data analysis tools.

The observations were as follows:

1. Relation of time devoted to self-study with the monthly pocket
money:

An inverse relation is evident, when plotting monthly pocket money
against the time devoted to self-study (hrs per week). It was observed
that on an average, college students receiving pocket money around
Rs.500 per month utilize about 30-50 hrs per week for self-study. On
the other hand, as the pocket money rises, study time falls to as low
as 5hrs per week. This analysis gives us an insight into student
psychology. It is certain that students get diverted with too much
money in hand, and education takes a backseat.

[IMAGE]

2. Relation between the number of movies seen in a month with the
pocket money received:

A clearly incremental graph is obtained when the number of movies seen
(per month) is considered alongside the monthly pocket money. With
monthly pocket money of Rs.500 an average student watches about 2
movies per month, while one receiving Rs.15000 can afford to watch
more than 10. From this we can infer that movies being a common
expenditure of college students, the more money is available, the more
movies are seen per month.

[IMAGE]

3. Variation of average pocket money on the basis of gender:

52 females and 51 males provided the 103 data entries. This uniformity
provides us the opportunity to obtain a value for their respective
average monthly pocket money. It is noticeable that an average female
receives a higher pocket money than an average male. While the average
pocket money of males is close to Rs.3000, that of an average female
is more than Rs.3500.

[IMAGE]

4. Variation in time devoted to self-study on the basis of gender:

It is a realised trend that females usually devote more time to
self-study than males. However, the results of our analysis do not
conform to it. As per our analysis males append about 19hrs per week
on self-study, while females approximately 13hrs. As per our analysis,
it was observed that females receive a higher pocket money than males
and also that with an increase in pocket money the time devoted to
self-study decreases. This could be a possible cause for the obtained
result and deviation from the trend.

[IMAGE]

5. Relation of Monthly Family Income with Monthly Pocket Money:

Distribution is always with respect to a whole. Similarly, the
apparent fact of pocket money given to children being dependent on the
income of the family is verified by the graph below. It is clear from
the graph that pocket money follows a direct relation with the family
income.

[IMAGE]


INFERENCIAL ANALYSIS

Inferential statistics basically relates the sample characteristics to
population characteristics. We take random samples from the
populations because we cannot take the entire populations for the
purpose of our study. Samples are simply the means to an end and not
an end in themselves. Statistical inference is concerned with making
inferences about the population parameters. Typical population
parameters are the mean, standard deviation, the area under the curve
between two values of a variable etc.

Inferences about Regression as a whole: Overall Significance

Using F-test

The F test is used to determine whether there is a significant
relationship between the dependent variable and the set of all the
independent variables. It helps us check whether the value of R-square
really indicated that the independent variables explains Y or has
happened just by chance.

"Is the regression as a whole significant?"

We see how all the Xi's taken together significantly explain the
variability explained in Y. Our hypotheses is

Ho: B1 = B2 = B3 ….. = Bk

Null hypotheses: Y does not depend on Xi's.

Hi: At least one Bi¹0

Alternate Hypotheses: Y depend upon at least one Xi's

In discussing the Variation in Y we look at three different terms, we
denote these by:

Three different Sums of Squares,

[IMAGE]

SST = Total Sum of Squares (i.e. explained part) = ∑ (Y - [IMAGE]) 2

SSR = Regression Sum of Squares (i.e. the unemployed part) ∑ (Y-[IMAGE])
2

SSE = Error Sum of Squares (i.e. the unemployed part) ∑ (Y-[IMAGE]) 2


These are related by Equation

"Decomposing the total Variation in Y"

SST = SSR + SSE

Which says that the total variation in Y can be broken down into two
parts :

Explained Part & Unexplained part.

Each of these squares has associated (n-1) degrees of freedom (n
observation 1) degrees of freedom because sample mean is fixed. SSR
has k Degrees of Freedom because there are 'k' independent variables
being used to explain Y.

Finally, SSE has (n-K-1) degrees of freedom because we used our 'n'
observation to estimate

(K+1) constants, a, b1, b2…………..bk.

If the null hypothesis is true the ratio below is equal to.

SSR/ k

F = ________________

SSE/ (n-k-1)


From the summary output: We see that SSR = 727000000 (with K=7 degrees
of freedom)

SSE = 378000000(with n-k-1=102-7-1= 95 degrees of freedom)

So, F = 727000000/7

378000000/95

= 26.14

the entries in the "MS" column are just the sums of squares divided by
degrees of freedom for 7 numerator degrees of freedom & 95-denominator
degree of freedom. The table tells us that 2.12 is the upper limit of
acceptance region. For a significance level of

α = 0.05.

Our calculated F value of 26.14 is far above 2.13 so we see that
regression as a whole is highly significant. We can reach the same
conclusion by noting that the output tells us that "significance F"=
1.31e-19

Inferences about an Individual Factor: Individual Significance

The z-test

The T Test is used to determine whether each of the individual
independent variables is significant. A separate t test is conducted
for each of the independent variables. The purpose of the t-test is to
see whether we can use the sample data to conclude that

The regression plane is derived from a sample and not from the entire
population. As a result, we cannot expect the true regression
equation:

Y = A+ B1X1+B2X2+………..+B kXk

(The one for the entire population)

To be exactly the same, as the equation estimated from the sample
observations,

Y = a + b1X1 + b2X2 +.…….+ bkXk

Even so we can use the value of b1, one of the factors, we calculate
from the sample, to test hypotheses value of B1, one of the factors of
the regression plane for the entire population.

We test the following Hypothesis about B1.

H0 : B1 = 0

Null Hypotheses

H1 : B1 ¹0

Alternate Hypotheses

If H0 is rejected, we will conclude that B1 ¹ 0 and that the two
variables have a statistically significant relationship. However, if H0
cannot be rejected [We reject H0 if (t <-ta/2) or if (t> ta/2)], we
would not have sufficient evidence to conclude that there is a
relation between the variables.

Age:

Here,

test statistic, t = 2.891083

t0.025 = 1.50

With 2.891083>1.50 (t0.025), we reject H0 and conclude at the 0.05
significance that B1 is not equal to zero.

The statistical evidence shows that there is a significant
relationship between age and monthly expenses.

Number of working parents:

Here,

test statistic, t = 2.155667

t0.025 = 1.50

With 2.155667>1.50 (t0.025), we reject H0 and conclude at the 0.05
significance that B1 is not equal to zero.

The statistical evidence shows that there is significant relationship
between Number of working parents with monthly expense of students.

Monthly income:

Here,

test statistic, t = 2.613987

t0.025 = 1.50

With 2.613987<>.50 (t0.025), we reject H0 and conclude at the 0.05
significance that B1 is not equal to zero.

The statistical evidence shows that there is significant relationship
between family monthly income and monthly expenses of students,

Number of siblings:

Here,

test statistic, t = -0.902742

t0.025 = 1.50

With -0.902742<1.50 (t0.025), we accept H0 and conclude at the 0.05
significance that B1 is equal to zero.

The statistical evidence shows that there is no significant
relationship between number of siblings and monthly expenses of
students,

Number of movies seen in a month:

Here,

test statistic, t = 3.142832

t0.025 = 1.50

With 3.142832>1.50 (t0.025), we reject H0 and conclude at the 0.05
significance that B1 is not equal to zero.

The statistical evidence shows that there is significant relationship
between Number of movies seen in a month and monthly expenses of
students.

Visits to restaurants per month:

Here,

test statistic, t = 5.421227

t0.025 = 3.96

With 5.421227>1.50 (t0.025), we reject H0 and conclude at the 0.05
significance that B1 is not equal to zero.

The statistical evidence shows that there is significant relationship
between Number of restaurant visits per month and monthly expenses of
students.

Time devoted to self study:

Here,

test statistics, t = -1.747169

t0.025 = 3.96

With -1.747169<1.50 (t0.025), we accept H0 and conclude at the 0.05
significance that B1 is equal to zero.

The statistical evidence shows that there is no significant
relationship between time devoted to self study and monthly expenses
of students.

Also, we use the P-value to test whether the factors are significant
explanatory variables or not. The entries in the column are
probability values for the two-tailed test of the hypotheses.

Ho: B3 = 0

H1: B3 ¹0

We only compare the probability value with athe significant level of
the test, to determine where QF is a significant variable of Y.

Testing the significance of an explanatory variable is always a
two-tailed test. The independent variable Xi is a significant
explanatory variable if "bi" is significantly different from zero,
that is, if to is a large positive or a large negative number.

Testing Hypothesis for independence of two categories though χ2

CHI square test

CHI square is used as goodness of fit test, it is most of the used as
a test of independence to determine if the paused observations
obtained on two or more nominal variables are independent of each
other or not. It is some times necessary to deal with the idea of two
variables being related in the sense that the value of one variable
depends upon the value of other corresponding variable.

Then the null hypothesis for independence can be tested by: -

[IMAGE] χ2 = ∑ (fo - fe)2

fe

Where:

Fo = Observed frequency

Fe = Expected frequency = row total*column total/100

∑ = summation overall cells

The degrees of freedom in a contingency table are given below;

df = (r-1) (k-1)

Where:

R = number of rows

K = number of columns

Relationship Between Family Income and Fathers Education.

H0 = 0: Null Hypothesis: no relationship between income and education.

H1 = Alternate Hypothesis: relationship between income and education.

[IMAGE]

[IMAGE]


fo

fe

fo - fe

x = |fo - fe| - 0.5

x2

x2 / fe

25

22.63

2.37

1.87

3.5

0.1546

6

9.61

-3.61

3.11

9.6721

1.0064

22

20.44

1.56

1.06

1.1236

0.0549

6

8.68

-2.68

2.18

4.7524

0.5475

10

10.22

-0.22

0.28

0.0784

0.0076

4

4.34

-0.34

0.16

0.0256

0.0059

6

8.76

-2.76

2.26

5.1076

0.583

6

3.72

2.28

1.78

3.1684

0.8517

8

11.68

-3.68

3.18

10.1124

0.8658

8

4.96

-4.04

3.54

12.5316

2.5265

2

2.19

-.19

0.31

0.0961

0.0438

1

0.93

.07

.43

0.1849

0.1988

6.8465

Solving the problem we get the value of χ2 as 6.8465

Looking at the value of χ2 from the table for 95% confidence (or α =
0.5) & at (6-1)(2-1) = 5 degrees of freedom, we get:

χ2 = 11.0705

Since our calculated value of χ2 is less than the critical value of χ2
i.e. 11.0705; we accept the null hypothesis and reject Alternate
hypothesis, concluding that there is no relationship between family
income and number of working members in the family.



Relationship between amount of time devoted to self study and number
of movies seen in a month
====================================================================

H0 = 0: Null Hypothesis: no relationship between time spent on self
study and number of movies seen in a month.

H1 = Alternate Hypothesis: relationship between time spent on self
study and number of movies seen in a month

Study Movies

1-2

3-4

5-6

7 or more

Total

<15

27

13

13

12

65

15-25

10

4

4

2

19

25-35

2

2

4

5

13

35-45

0

1

2

0

3

>45

3

1

0

0

4

Total

42

21

22

19

104

fo

fe

fo - fe

x = |fo - fe| - 0.5

x2

x2 / fe

27

27.3

-0.3

0.2

0.04

0.0014

13

13.65

-0.65

0.15

0.025

0.0019

13

14.3

-1.3

0.8

0.64

0.0447

12

12.35

-0.35

0.15

0.025

0.002

10

7.98

2.02

1.52

2.3104

0.2895

4

3.99

0.01

0.49

0.2401

0.0602

4

4.18

-0.18

0.32

0.1024

0.0245

2

3.61

-1.61

1.11

1.2321

0.3413

2

5.46

-3.46

1.99

3.9601

0.7253

2

2.73

-0.73

0.23

0.0529

0.0194

4

2.86

1.14

0.64

0.4096

0.1432

5

2.47

2.53

2.03

4.1209

1.6684

0

1.26

-1.26

0.76

0.5776

0.0458

1

0.63

0.37

0.13

0.0169

0.0268

2

0.66

1.34

0.84

0.7056

1.0691

0

0.57

-0.57

0.07

0.0049

0.0086

3

1.68

1.32

0.82

0.6724

0.4002

1

0.84

0.16

0.34

0.1156

0.1376

0

0.88

-0.12

0.38

0.1444

0.1641

0

0.76

-0.76

0.26

0.0676

0.0089

TOTAL

5.1829

Solving the problem we get the value of χ2 as 5.1829

Looking at the value of χ2 from the table for 95% confidence (or α =
0.5) & at (5-1)(4-1) =12 degrees of freedom, we get:

χ2 = 21.0261

Since our calculated value of χ2 is less than the critical value of χ2
i.e. 21.0261; we accept the null hypothesis and reject Alternate
hypothesis, concluding that there is no relationship between number of
movies seen in a month and time spent on self study.


EXCEL FUNCTIONS USED

Alongside the essential functions of regression, t-test, f-test, chi
square test, mean, certain other functions were also used to make
interpretations and calculations easier. An example of this is the
sort function.

Use of 'Sort' Function:

The Y factor, namely the monthly pocket money was arranged in
ascending order. This Excel function provided the convenience of
analysing whether the sample space had been appropriately selected, so
as to represent the population. The data collected was significant as
it included a broad range that varied between Rs. 500 to Rs. 15000 per
month. Also was identifiable a gap in the incremental trend of the
data collected. The data does not include any entries with pocket
money ranging from Rs. 5500 to Rs. 8000. A method to rectify this is
by entering all useful data simultaneously as it is obtained. However,
in this research the impact of this drawback is reduced as the number
of questionnaires considered was many. i.e. 103

[IMAGE]

This function was also used to segregate the data on a gender basis.
Dummy variables were used to depict this variable. Females were
represented by 1, and the males with a 0 as for binary coding. These
values were then sorted to obtain a data segregated on the basis of
gender. This made further analysis on this basis easier.

[IMAGE]


CONCLUSION

From a sample space of around 100 students we made inferences about
the various factors influencing the pocket expenses of students.
Subsequent to the analysis, it was notices that certain factors have a
direct relation with monthly pocket money while others demonstrate an
inverse relation.

Variables with direct relation:

· Age:

As this questionnaire was targeted at the college students the age
group selected was 17 - 24. It was observed that in this age group
your pocket expenses increase with age as a rise was observed in the
expenditure on education and entertainment.

· Working parents:

It was observed that both parents working, leading to greater family
income had a direct impact on the pocket money of students. Also these
students were observed to be more outgoing and spent major part of
their pocket expense on entertainment.

· Entertainment:

It is however obvious that greater the pocket money greater would be
the money spent on entertainment. As in the questionnaire we divided
entertainment in various sub heads such as movies, eating out, money
spent on gym and health club etc, we observed the major portion of
money spent was entertainment.

Variables with Indirect Relation:

· Number of siblings:

From the observed data we concluded that more the number of siblings
lesser is the pocket many i.e the number of siblings and the monthly
pocket money of students has an inverse relation. It is thus seen the
more the number of siblings, the money gets distributed hence lesser
money for each student.

· Time devoted to self-study:

Our analysis showed that students who spend more time on self study
spend less on entertainment and hence have quite reasonable monthly
expenses. Thus an inverse relation is seen between both variables.


APPENDIX

SURVEY FORM NO.:

The Questionnaire:

FACTORS INFLUENCING POCKET EXPENSES OF COLLEGE STUDENTS

All the information provided by you will be strictly used for academic
purposes only and will be kept confidential.

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Name:

____________________________________

Age:

_______ yrs

Gender:

§ M

§ F

Contact (email/phone no.):

___________________

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1. Who is/are the working parent(s) in your family?

§ Father

§ Mother

§ Both

2. What is the highest level of education of your parents?

Father :

§ Secondary School

§ High School

§ Graduate

§ Postgraduate

Mother :

§ Secondary School

§ High School

§ Graduate

§ Postgraduate

3. What is the main source of your family income?

§ Service

§ Self- Employed Earnings

4. What is your family's average monthly income? (From all sources)

§
§ Rs.20,000 - Rs.40,000

§ Rs.40,000 - Rs.60,000

§ Rs.60,000 - Rs.80,000

§ Rs.80,000 - Rs.1,00,000

§> Rs.1,00,000

§ If other, please specify _______________________________

5. How many siblings do you have?

§ 0

§ 1

§ 2

§ 3

§ 4

6. What is your average monthly pocket money?

§ Rs.500 - Rs.1,000

§ Rs.1,000 - Rs.2,000

§ Rs.2,000 - Rs.3,000

§ Rs.3,000 - Rs.4,000

§ Rs.4,000 - Rs.5,000

§ Rs.5,000 - Rs.6000

§ If other, please specify __________________________

7. Do you own a personal vehicle?

§ Yes

§ No

8. How many movies do you watch in a month? _____ (per month)

9. How many times do you visit to a restaurant/eating joints in a
month? _____ (visits per month)

10. Do you visit a fitness centre (gym/health club)?

§ Yes

§ No

If yes, how many days in a week _____ (days per week)

11. How much time do you devote to self study? _____ (hours per week)

Signature: _____________

Date: _________________

----------------------------THANKYOU --------------------------


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