STATISTICAL ANALYSIS OF ROAD ACCIDENTS

(A CASE IN ENUGU STATE FROM 2000 – 2008)

 

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ABSTRACT

This project is in compliance with one of the task, I have to shoulder in order to be awarded the Higher National Diploma Certificate in statistics department from Institute of Management and Technology, Enugu, during my final year in the Polytechnic 2004/2005 session  emphasizing on Statistical Analysis of Road Accident in Enugu from 1993 to 2000.

Road accident has been of great social and economic concern.  It has became a total topic for scientific investigation.  The number of deaths on the road today, particularly on the major roads of rural-urban areas are what motivated me in writing this project.

This study is essentially based on the Statistical Analysis of Road Accidents recorded in Enugu rural-urban roads from 1993 to 2000 with the objectives to; identify the causes of road accidents in Enugu and compare the attendant fatalities/deaths, ascertain whether the causes of road accidents are unrelated with vehicles, establish the trend of road accident over the years, investigate, whether there is any seasoned pattern of occurrence of road accident and trend and/or investigate whether there is any seasonal pattern of the attendant deaths and trend, and recommend methods or ways of reducing road accidents to the Enugu State government, the institutions concerned with traffic management and enforcement of the laws within the geo-political entity and the road users, and the federation in general.

The project work is divided into five chapters.  Chapter one gives the introduction, socio-economic effects of road accidents, aims and objectives, scope and limitation, significance of the study, sources of data and the problems of the data collection.  Chapter two covers the literature review.  Chapter three is concerned with the methodology.  Chapter four deals with the data presentation and analysis.  Finally, chapter five covers the findings, conclusion and recommendation on the way forward.

 

 

 

CHAPTER ONE

• INTRODUCTION

In the world today, transportation which is the conveyance of goods and passengers from one phase to another or the movement of commuter and their goods, produce and products, and/or they themselves from one location to another have played an important role in the development process, thus, serving as one of the aspects of developmental change indicators and structural well-being of the society and government among other sectors or areas of the world socio-economic development.  It provides room not only for transaction of business to take place, market possibility for our goods, produce and products produced, but also makes it possible for such to reach the find consumer(s).

 

For instance, in Costa Rica, before the inter America – highway was constructed, driving beed cattle on the hoof from grazing lands to San Jose often resulted in a 40 percent less of weight, and imports were necessary to supply local needs.  But with and weather highway, it was possible to deliver truck-traider units of cattle over night, and costs Rica become self-supporting in meet.  Also in Bolivia, the highway from cochabamba to santa cruz reduced the travel time in the rainy season from several weeks to fifteen hours and provided a link between the country’s food supplies and its people.  Until then the price of home-grown rice was 50 percent higher than the imported rice because of the high cost of transport.  Furthermore, transportation as an integral part of national production and distribution system calls for its development, improvement and better network system as to necessitate or provide a means of servicing domestic and international market.

 

This is of primary importance in the early stages of economic development because it promotes an accumulation of capital, which allows the economy to progress from the subsistence level at which most production is consumed locally.  Therefore, transportation and other government programmes such as education and health care, necessarily compete for public expenditures particularly in the underdeveloped countries.

From the foregoing, the developed nation are efficient and effective in transport business as a result of their improvement and technological advancement over the years.

Nigeria has one of the most modern and best development transport systems – roil, road, air and in-land waterings which transverse the length and breath of the country to link the industrial, commercial, and agricultural centers, that is to say, transportation in Nigeria is traditionally under four major mades namely;- road, rail, water and air.  However, in this study, the researcher zeros down to road transport.

In Nigeria road network, roads are categorized into three; the truck A roads which is the responsibility of the federal Government, truck B roads which is the responsibility of the state Government and the third category-truck C which is the responsibility of the local Government.  Whether truck A, truck B, and truck C roads, these roads are used by the motorists, cyclists, pedestrians either to convey their passengers, goods, produce, products or to reach, transact and communicate with another n different destination.  Road transportation has not only been discovered as the cheapest means of transportation but also provides door-to-door transport services and delivery of goods.

 

But apart from road congestion which is symptom of the availability of insufficient road space to satisfy, with but difficulty, all demands made upon it, road accident is another difficulty task in traffic management schemes and has been of much concern to various governments of our timer hence, the concern of any well-organised government is how to identify and minimize (if possible curb) the high rate of accidents on our roads today.

 

We are aware of the number of deaths on the highway being recorded these days.  This places a question mark on the value we attach to human life and property.  It is clear on the basis of logic backed by observations that certain people have worse accident records than others.  This research will investigate why it is so and would also proffer suggestions to check the ugly trends people who drive recklessly or dangerously are potential victims of accidents and are prone to such conditions.  They also constitute a nuisance to the society.

 

Most accidents have been caused by a whole lot of actors.  Prominent among them are as listed below:

1. Over-Speeding: Some times may be due to greediness or the tendency to drive as many turn as possible always want to be at the head of others, without considering the consequences.  By so doing they neglect road signs warnings and road traffic regulations and laws.  Thus, the risk of some dangerous.
2. Drugs/Alcohol: The side effects of drugs or alcohol our body cannot be over emphasized.  These cause drowsiness and finally sleep when during.  They lead to wrong calculations and loss of regard to lvies of human beings and property of such driver concerned.  Some causes excessive alertness and nervousness, loss of control and finally a breakdown of the body system of such person involved.
3. Roads (Road Accidents Immuned Delusion Syndrome): Some drivers because they have driven a particular vehicle for years, taxy develop the feeling that they have overmastered the vehicle and also fully experienced do believe that they cannot be involved in road traffic accident, others or other drivers because of their belief either a shrine, ring, talisman, etc. do believe that they cannot be involved and/or die in road accident, they drive without regard to road traffic regulations and other road users.
4. The Road: The construction of the road matters a lot.  Roads with multiple bands experience many accidents.  Poorly constructed road witness many accidents e.g. presence of informal bymps, very narrow roads.  Roads that are poorly maintained cause a lot of accidents.  The absence of road signs also contributes to road accidents e.g to show construction sites, narrow bridges, cross roads, bumps, “T” junction etc.
5. 5. Negligence of road Signs: Most Nigeria drivers are so illiterate that they cannot read road signs and as such endanger their lives and the lives of others and property.
6. Aggression: This is psychological.  Also result of or may be due to lack of sleep in the previous night due to one problem or the other.  The driver then wake up annoyed and aggressive.  He jumps into the vehicle without the morning drills, quarrels with the vehicle passengers, co-drivers and road traffic officers etc. thus the risk of accident victimized and even others.
7. The Weather: This comprises the rain and the sun and their effects on the roads.  The rains wet the roads and make them slippery therefore, tyres treads loase grip of the roads and render braking almost impossible as and when desired.  The sun heats up the tar on the road which in tam heats up the tyres.  When this happens, weak tyres tends to burst very easily.  Both conditions causes accidents on our road if not observed.
8. Topography: This includes hilly, rocky forest and savanna areas.  Areas where the roads run in between hills particularly with dedling rock constitute a lot danger to road users.  Where such exits, viewing distance are shortened, the rocks can fall into the road at any time and cause accidents.  Likewise where roads run across forests, trees, and/or their branches, many fall into the road and where this is not noticed in a good time, they can cause serious accidents.  Animal shiving is the forests can cross the roads at any time while grazing animals common in the savanna requires can also  cause accidents.
9. Carelessness of Pedestrians: The other road user that is seen as the commonest – the pedestrian(s) may out of illiteracy and inexperience in using the road disobey the road traffic sign by crossing when it is not due for him or her to do so.  Or cross the busy road without looking left or tight as to see when the road is free for crossing.
10. Foods: It takes many drivers time to understand the effect of some foods on their body.  Most eat one type of food because others do.  They fail to understand that, while some people or such people will be active after a heavy food, others or themselves imitating feel dull and will be sleeping after such a heavy food and thus, endangering their lives and property while driving.

 

1.1     SOCIO-ECONOMIC EFFECTS OF ROAD ACCIDENTS

Several aspects of road transport negative impact (road accident) on the society have already been discussed.  Some additional negative effects deserve mention.  Road accidents have significant effects, which they impact.  Adversely on the economic and social welfare of a nation.  The effects on the economy usually take the form of costs which under certain circumstance can be measured.  Some of these costs; private costs are borne by those responsible for the accident, while others are social in nature in that society as a whole bears them.  In this section, the study examines specific effects of road accidents.

1. Traffic hold-up and associated waste: When an accident occurs, the most easily observed effect is a rapidly built-up traffic holdup.  In the process, fuel is wasted, engines are overheated, delays lead to lost business and social opportunities.  The direct effect is a showed down and more expansive business transactions.
2. Destruction of motor vehicle: Road accidents usually entail the complete destruction of motor vehicle involved. In some cases, the vehicles are salvaged at considerable cost to owners.  In Nigerian environment, accidental vehicles are either left on the scene of accidents indefinitely or are towed away to police stations where they are similarly abandoned.  The implication of this practice is that scrap value of such vehicle is lot to the economy and stock of transportation, facilities necessary to move people and goods from place to place is reduced.  The opportunities for realizing gains from within an integrated economic systems are lost, and the welfare of citizen earlier mentioned corresponding reduced.  Loss to the economy arising from road accidents is easily measurable.
3. Destruction of transport infrastructure: Accidents destroy valuable road transport infrastructure whose replacement would cost multiples of the original capital expenditure.  These costs are significantly foreign exchange are imported.  Components of transport infrastructure that may be damaged include;
4. Roads
5. Bridges

• Culverts etc

Thus, resulting to capital reduction instead of capital accumulation.

4. Destruction of other infrastructure: Road accidents also destroy other infrastructure such as telecommunication poles and wires, electricity poles and transformers, real estate including residential and office buildings.  Damage to these infrastructure disrupt electricity supply, telecommunications services and normal office facilities; all these tend to show down normal economic and social transactions with adverse consequences on the quality of life.
5. Short supply of goods: Accidents cause the damage or destruction of goods being transported. The loss reduces total quantity of goods available for consumption by the final consumer(s) and reduces profits for or made by the companies whose goods are destroy.  Where insurance cover is provided, cost of damage are passed on the insurance companies thus, reducing their capital gain if the goods are essential for normal subsistence, large scale destruction may necessitate importation which would either place a downward pressure on foreign exchange rates or lead to substantial devaluation of the exchange rate in a system of  flexible exchange rates.
6. Medical bills for treating accident victims: Medical bills of accident victims are some of the adverse effect of road accidents.  Treatment in the orthopedic hospitals is time-consuming and expensive, after discharge of patients, the ability of such a person to perform duties is usually reduced.  This has adverse effect on production in the economy.

 

• AIMS AND OBJECTIVES

The main objectives of this project are to;

1. Identify the causes of road accident in Enugu and compare the attendant fatalities/deaths.
2. Ascertain whether the causes of road accident are unrelated with vehicles.
3. Investigate whether there is any seasonal pattern of occurrence of road accidents and trend and/or compare the number of cases.
4. Establish the trend of road accident over the years.
5. Recommend methods or ways of reducing road accidents to the Enugu State Government, the institutions concerned for traffic management and enforcement of the laws within the geo-political entity and the road users.

 

• SCOPE AND LIMITATION

The scope of this study is restricted to Enugu Rural Urban Areas (Enugu State) only on the account of the following constraints;

1. The time available for this research work is limited to cover other states.
2. The resources available were very inadequate to expand the scope.

 

 

 

 

• SIGNIFICANCE OF THE STUDY

This study would help the government, the general public, the Nigerian Police Force, the Federal Road Safety Commission and other agencies concerned with safety on our roads in the following ways:

1. It will help the Federal Road Safety Commission and other authorities concerned with similar assignment to assess their performance over the years.
2. It will help the Federal and state governments particularly Enugu State to articulate policies on road transportation and safety, such policies will form the basis of planning the socio-economic infrastructure necessary to ensure safety and enhance the performance of road users.
3. it will help the Federal Road, Safety Commission and other institutions concerned organizing sensitization workshop on seminars programmes for road users ascertain the positive impact of such workshop or seminar being organized.
4. It will awaken the sense of responsibility of road users and government.
5. It will help reduce or put to a stop the ill attitude poster by some of the law enforcement agencies (the Nigerian Police N20 syndrome) hindering the reduction of road accident.

 

• SOURCES OF DATA COLLECTION

The data used for this project work were collected internally in secondary form.  Secondary data imply statistical materials or information not originated or obtained by the investigator himself, but obtain from someone’s record or published source such as the central bank, government agencies and non-governmental duties such as universities, research institutes etc.  The data were however, provided by Federal Office of Statistics (FOS) Enugu Division and the Federal Road Safety Commission, Enugu Sector Command.

 

• PROBLEMS OF THE DATA COLLECTION

The problems encountered during collection of data cannot all be stated here.  This research work posed a lot of problems.  Since the researcher did not originally collect the data, there was mistrust between the primary users and the secondary user of the data.  It took me a lot of money, time and energy traveling from my destination to the office of the Federal Office of Statistics (FOS) and that of the Federal Road Safety Commission all in Enugu, so as to get the relevant data for this research work.  This made me to miss most of my lecture hours and also disappointed my supervisor Mr. Pius Ugwu by not coming when I promised to see him several times.

It was very difficult to collect the relevant data from these offices because they said that they couldn’t release the data for security reasons.  But after presenting letters from my Department Head Mr. Nwagbara G.P. dated 4^th July, 2005, the desired information was given to me.

 

 

 

Continue reading STATISTICAL ANALYSIS OF ROAD ACCIDENTS (A CASE IN ENUGU STATE FROM 2000 – 2008) →

STATISTICAL ANALYSIS OF STUDENTS’ EXPENDITURE IN TERTIARY INSTITUTIONS

(A CASE STUDY OF IMT ENUGU 2004/2005 SESSIONS)

 

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ABSTRACT

        The aims of this project are to describe the various ways in which students spend their money and to advise them on how to spend their money judiciously.

About three hundred and sixty questionnaires were distributed randomly to six schools and one hundred and forty valid returns of questionnaires were gathered.

From the analyses, it was discovered that despite the hard earned income of parents, most students insist on spending their money extravagantly.  This is mostly found commonly   the female students.  According to the data age was identified as one of the major factors which influence the spending habit of students.  Students below twenty – five years spend higher than students above twenty-five years.  We also noted that students whose parents are wealthy spend much higher than students whose parents are averagely rich.

Finally, students should judiciously spend money only on important items and should avoid ostentations spending.

 

 

TABLE OF CONTENTS

TITLE PAGE

APPROVAL PAGE

DEDICATION

ACKNOWLEDGEMENTS

ABSTRACT

APPENDICES

LIST OF T ABELS

TABLE OF CONTENTS

CHAPTER ONE

• INTRODUCTION
• AIMS AND OBJECTIVE
• DEFINITION OF TERMS AND CONCEPTS

CHAPTER TWO

2.0   LITERATURE REVIEW

CHAPTER THREE

• SOURCE OF DATA
• SAMPLING FRAME

TABLE 1  THE DISTRIBUTION OF REGULAR STUDENTS

• SAMPLING PLAN
• REASONS FOR STRATIFICATION
• METHOD OF DATA COLLECTION
• PROBLEMS ENCOUNTERED DURING DATA COLLECTION
• PILOT SURVEY
• ASSUMPTION FOR STRATIFICATION
• TABLE 2 ALLOCATION OF QUESTIONNAIRES (PILOT SURVEY) TO THE SIX SCHOOLS A ND THEIR VALID RETURNS
• DETERMINATION OF VARIANCE
• DETERMINATION OF SAMPLE SIZE
• THEORITICAL FRAME WORK

CHAPTER FOUR

ANALYSIS

• ANALYSIS INVOLVING TEST OF TWO MEANS
• ANOVA INVOLVING TEST OF TWO MEANS

CHAPTER FIVE

FINDINGS, RECOMMENDATION AND CONCLUSION

REFERENCES

APPENDIX

QUESTIONNAIRE

 

 

CHAPTER ONE

INTRODUCTION

1.1   BACKGROUND OF TH STUDY

        Spending is referred to the total expenditure of an individual, government or an organization.

Having said this, government can spend money for projects like building of schools, construction of roads, establishments of electricity, etc and these erupt development in our country.  Parents also later for the need of their children and enrich them with huge sums of money as pocket money.  Some of the student’s need which propel them to spend could be enumerated thus: school fees, hotel fees, feeding, transport fares, drinks and educational materials, etc.

Taking you years backs, Nigeria had a good economy.  Government and parents spent much of their money without any pains.  Students and that time used money recklessly because there was a good economy and balanced with monetary value in the market.

From 1980 till now, we have been experiencing our increasing an unexpected inflation of goods

 

1.3   DEFINITION OF TERMS AND CONCEPTS STATUS 

It is the social or professional position of somebody in relation to others:

Income:

This is the earning of an individual in taking part in production of goods and services.

Expenditure is broken into meaningful and logical categories namely:

A      Food:

It is anything we eat for the nourishment and growth of the body.

B      Clothing and Foot-Wears

Clothing are those things that we use to cover our body because of cold and diseases. While foot – wears are those things that we wear on our feet so as to prevent us from wound and diseases.

1. Drinks

It is either alcoholic or non-alcoholic liquor.

1. Make-ups

These include such thing as powder, pomerde, up-sticks, eye-pencil, etc.

1. Educational Materials

These are materials used for academic works like books, mathematical sets, drawing sheets, calculators, etc.

1. Projects

This includes field-works, research – work, term paper, etc.

1. Hobbies

It is occupation for one’s leisure time, for example reading, sports and listening to music.

1. Entertainment

This includes film show, parties, cinema, which we use for enjoyment and relaxation of the body.

 

 

 

CHAPTER TWO

2.0   LITERATURE REVIEW

        Some people had said their opinion and contribution on this project.  They had recommended that students should spend judiciously and should avoid unnecessary spending.

According to professor Lionel Robbins, a renowned social scientist and an economist, in are of his works.  “Fundamentals of Economics (1993)”, noted that human wants were not satiable, but the resources with which to satisfy them were scarce.  In this respect, one has to make a good scale of preference and choose    the most important to maximize utility.

Kenneth C. Agbasi (1988), Head of computer science of Nnamdi Azikiwe University, Awka at the commission of IBM computer commended the effort of National Association of Computer Science Student (NACOSS).  In his work he said “the president hard never wasted the departmental money but he used it to purchase computer for the departmental usage”.

Obasi P.V. (1992) made a research on “ students’ expenditure on consumption of food beverages” her work was generally good, particularly her analysis, she verified that students’ expenditure on carbonated and non-carbonated food beverages was independent of sex.  From her analysis of variance, she said that quantities of carbonated drinks consumed by students depends on school and the rate at which male students taken alcohol beverages was high.  In her recommendations, she said that students should abstain from alcohol such as: beer, rum, etc, because of their adverse effect on health.

Finally, not much research work has been done on this project available written works on this project are few and students should know how to spend them money on those items need and also their parents should support their fully financial and in other things which will help them towards their studies.

 

 

CHAPTER THREE

RESEARCH METHODOLOGY

3.1   SOURCE OF DATA

        This survey is carried out in the Institute of Management and Technology Enugu.  Primary data is used and questionnaires are distributed to the six schools at randomly.

 

3.2   SCOPE OF STUDY

        The scope of study covered only the regular students of IMT, Enugu of 2004/2005 session.

 

3.3   SAMPLING FRAME

        It is  the comprehensive lists of all the regular students of Institute of Management and Technology, Enugu from 2004/2005 session, and obtained from admission’s office.

TABLE 1:         THE DISTRIBUTION OF REGUALR STUDENTS

S/NO	SCHOOLS	NO OF STUDENTS
1 2 3 4 5 6	RAM COMM ARTS FIN. STUDIES ENGR TECH SSYTE	6154 3490 7270 4474 2009 192
	TOTAL	23589

 

 

3.4   SAMPLING PLAN

        Stratified random sampling is used for this survey.  According to John E. Frend (Fourth Edition), 1988 when population can be sub divided in a number of subpopulation, or strata each of which is relatively uniform or homogeneous.

In this kind of sampling, we divide the population into a number of non-overlapping homogenous subpopulation to which we their allocated certain portions of the total sample.

 

3.5   REASONS FOR STRATIFICATION

        Stratification was used because the different schools can be regarded as homogeneous subpopulations in which the units (students) are non-overlapping.  A student belongs to one and only one stratain (school).

Stratification provides estimates of population parameters with high degree of precision.

Administrative convenience also necessitated the use of stratification.

In stratified random sampling we may apply different sampling methods to be considered more quotable than different sections of population.

 

3.6   METHOD OF DATA COLLECTION

        Questionnaire technique is used to obtain data from students. Three hundred and sixty questionnaires were distributed randomly to each school for the students to fill about one hundred and fourty valid returns were gathered.

 

3.7   PROBLEMS ENCOUNTERED DURING DATA COLLECTION

Many problems were encountered during data collection stage.  The first was the problem of going to campus II repeatedly to collect data from Admissions Office IMT, Enugu.

Secondly, there was the problem of non-response. Some students’ refused to fill the questionnaires, claiming that they had no time. Some students filled the questionnaire wrongly and ticked more than once one some spaces.

 

3.8   PILOT SURVEY

From practical point of view, a small pre-test method was carried out on the survey.  It has helped to decide upon effective techniques of asking questions which helped to improve the quality of the questionnaires.  It also showed problems and troubles that would come out before the main survey.

The sample size was estimated from the pilot survey.  A total of eighty questionnaires were distributed to the six schools proportionally, using Nigeria’s allocation formular given as:

n_n     =      nN_n

                  N

Where:

n      =      Sample size

N      =      Total number of students

n_n       =      The number of questionnaires allocated to

each school.

N_n    =      The total population in each school.

 

3.9   ASSUMPTION FOR STRATIFICATION

1. The stratum sizes are known
2. The frame for selecting a sample
3. The population units are non-overlapping

 

 

 

 

3.10 TABLE 2: ALLOCATION OF QUESTIONNAIRES (PILOT SURVEY) TO THE SIX SCHOOLS AND THEIR VALID RETURNS

S/NO	SCHOOLS	NO OF STUDENTS	ALLOCATIONS	VALID RETURNS
1 2 3 4 5 6	BAM COMM. ARTS FIN. STUDIES ENGR TECH SSVTE	6154 3490 7270 4474 2009 192	25 18 20 9 60 2	23 10 16 6 3 2
	TOTAL	23589	80	60

 

 

3.11 DETERMINATION OF VARIANCE

The summaration of average monthly feeding expenditure by the valid returns to students were recorded.  From the results, the variance was computed using the formular below.

 

S²     =      n²     V (yest)     =      V(Y)

Where

n²             =      Sum of the n stratum

V(yest)      =      the variance of the overall mean

population

=      å  W_n²      S_h² (I – f_h)

h=i                 n_n

W_h    =      Stratum weight of the population size

S²     =      The total variance of the population

 

3.12 DETERMINATIONM OF SAMPLE SIZE

The estimated sample size was computed from the pilot survey.  For the estimation of the sample size n the formular below was used (Proportional allocation)

n      =            N S²  

S² + N e²/4

Where

N      =      The total number of students under study

S²     =      The population variance

e²     =      Error

n      =      The total number of questionnaires.

 

3.13 THEORITICAL FRAME-WORK

The analysis of variance (ANOVA) is used in order to compare the mean Vi of several independent populations, that is to test the equality of means.

 

3.14 ANALYSIS INVOLVING TEST OF TWO MEANS

This analysis was carried out o test for whether there is a significant difference betweens the two means of students expenditure.

 

 

 

 

CHAPTER FOUR

4.0   ANALYSIS

4.1   ANALYSIS INVOLVING TEST OF TWO MEANS

This analysis was performed in order to findout whether there is a significant difference betweens the two means of students’ expenditure on food.

1. H₀: m_A     =      m_B (female expenditure = male

expenditure)

H₁:   m_A      ¹      m_B     (Female expenditure ¹ male

expenditure)

Here n_A     =      35            ,       X_A       =      5463

S_A       =      5502                        n_B    =      35

X_B    =      3886                ,       S_B    =      4465

Z      =              X_A    –       X_B

S_A²   +      S_B²

n_A               n_B

 

 

 

 

Z      =              5463                –       3886

5502²       +      4465

35                     35

Z      =      1577

1197.71

 

Z      =      1.3   (computed Z = statistic)

 

Conclusion:

The critical Z = score at the 5% level of significance is 1.96 (from the normal distribution table).  Since the computed Z value is less than the table value, we accept H₀ and conclude that average female expenditure on food is not significantly different from average male expenditure on food.

2. To test whether there is a significant difference between male students average expenditure and female students average expenditure on clothing’s and foot wears.

 

H₀:   m_A     =      m_B (female expenditure = male

expenditure)

H₁:    m_A    ¹      m_B     (Female expenditure is not the

same as male expenditure)

Here n_A     =      35            ,       X_A       =      2149

S_A       =      2289                        n_B    =      35

X_B    =      2130                ,       S_B    =      2279

Z      =              X_A    –       X_B

S_A²   +      S_B²

n_A               n_B

 

Z      =              2149                –       2130

2289²       +      2279²

35                     35

Z      =      0.04 (computed Z = statistic)

 

Conclusion:

The critical Z = score at the 5% level of significance is 1.96 (from the normal distribution table).  Since the computed Z value is less than the table value, we accept H₀ and conclude that average female expenditure on clothing and footwear is not significantly different from average male expenditure on the items

3. To test whether there is a significant difference between female and male expenditure on drinks.

H₀:   m_A     =      m_B (female expenditure on drinks is

sacars)

H₁:   m_A      ¹      m_B     (They are not the same)

Here n_A     =      35            ,       X_A       =      437

S_A       =      470                  n_B    =      35

X_B    =      299          ,       S_B    =      310

Z      =              X_A    –       X_B

S_A²   +      S_B²

n_A               n_B

 

Z      =              432          –       299

470²         +      210²

35                     35

Z      =      133

95.17

Z      =      1.4   (computed Z = statistic)

 

Conclusion:

The critical Z = score at the 5% level of significance is 1.96 (from the normal distribution table).  Since the computed Z value is less than the table value, we accept H₀ and conclude that average female expenditure on drinks is not significantly different from average male expenditure on drinks.

4. To test whether there is a significant difference between female and male students’ expenditure on educational materials.

H₀:   m_A     =      m_B (female expenditure equal male

expenditure)

H₁:   m_A      ¹      m_B     (Female expenditure is not

equal to male expenditure)

Here n_A     =      35            ,       X_A       =      3885

S_A       =      13119                      n_B    =      35

X_B    =      2279                ,       S_B    =      265

Z      =              X_A    –       X_B

S_A²   +      S_B²

n_A               n_B

 

Z      =              3883                –       2279

13119²     +      2651²

35                     35

Z      =      1604

2262

 

Z      =      0.71 (computed Z = statistic)

 

Conclusion:

The critical Z = score at the 5% level of significance is 1.96 (from the normal distribution table).  Since the computed Z value is less than the table value, we accept H₀ and conclude that average female expenditure on educational material is not significantly different from male expenditure on educational material.

5. To test whether there is a significant difference between male students average expenditure and female students average expenditure on others.

Here n_A     =      35            ,       X_A       =      2259

S_A       =      3422                        n_B    =      35

X_B    =      1703                ,       S_B    =      1849

Z      =              X_A    –       X_B

S_A²   +      S_B²

n_A               n_B

 

Z      =              2259                –       1703

3422²       +      1844

35                     35

Z      =      556

657

 

Z      =      0.85

 

Conclusion:

The critical Z = score at the 5% level of significance is 1.96 (from the normal distribution table).  Since the computed Z value is less than the table value, we accept H₀ and conclude that male expenditure on others are not the same to females’ expenditure on others.

 

4.2   ANOVA

        To compare the mean Vi of several independent populations, that is to test the equality of means.

TABLE AVERAGE MONTHLY SPENDING OF STUDENTS’ IN RELATION TO THEIR PARENTS’ STATUS

Parents’ Status	Food	Clothing and food wears	Educational materials	Drinks	Other
Civil Servant Teaching Trading (Business) Others	3409   3309 6005   3718	3988   4266 7739   3166	3245   3030 3405   2768	267   308 455   292	2461   1909 3813   1732
Tj	16441	19159	12448	1322	9913

 

Xijk  =      m + ai + bj + eij

Assumptions

1. åxij_k =      åxij_k         =      åxij_k         =      0
2. åai =      åbj           =      0
3. åeij W      N(o,e²)

Calculations of the sum of squares

1. SST =      åxij²         =      243130067
2. SSm = T²     . . .   =      C

N

=      59283²

20

C      =      175723704.5

3. SSA =      SSai =      åTi²  –       C      =      Ci – C

k

=      13370² + 12820² + 21417² + 11676²

6

=      187625233      –       175723704.5

=      11901528.5

4. SSB = SSbj =      åTj²  –       C = Cj – C

=      16441² + 19159² + 12448² + 1322² + 9913

4

=      892341719

4

=      223085429.8   –       175723704.5

=      47361725.25

5. SSE =      SSeij                =      Cij – C – Ci – Cj

=      243130067 + 175723704.5 – 187625233 – 223085429.8

=      8143158.7

ANOVA TABLE

MS	SV	d.f	SS
2975382 15787241 678592	Constant (m) Parents’ status (ai) Item (bj) Error Total F – ration 4.38 23.26	1 4 3 12 20	175723704.5 11901528.5 47361725.25 8143108.7 243130067

Conclusion:

Since the f-ratio is greater than the table value, we reject H₀ and conclude that the average spending of students from various parents’ status is not same.  And also since fcal = 23.26 m 3.49 = F (0.05,), (3,12) we reject H₀ and conclude that the average expenditure of students on items are not same.

TABLE AVERAGE MONTHLY SPEEDING OF STUDENTS BY AGE GROUP

Age	Food		Drinks		Others	Total
Under 20 yrs 20-24 yrs 25-29 yrs 30-above	5960 6218 3205 2965	2733 2148 1798 1700	524 476 257 239	4253 5553 2468 2828	2835 2685 2243 2130	17305 17080 9971 9862
Tj	18348	8379	1496	15402	10893	54218

 

 

 

 

Xijk  =      m + ai + bj + eij

Assumptions

1. åxij_k =      åxij_k         =      åxij_k         =      0
2. åai =      åbj           =      0
3. åeij W      N(o,e²)

Calculations of the sum of squares

1. SST =      åxij²         =      206575518
2. SSm = T²     . . .   =      C

N

=      54218²

20

C      =      146979576.2

3. SSA =      SSai =      åTi²  –       C      =      Ci – C

k

=      17305² + 17080² + 9971² + 9862²

5

=      787869310

5

=      157573862      –       146979576.2

=      10594285.8

4. SSB = SSbj =      åTj²  –       C = Cj – C

=      18348² + 8379² + 1496² + 15102² + 10893²

4

=      755822614

4

=      18895563.5     –       146979576.2

=      41976077.3

5. SSE =      SSeij                =      Cij – C – Ci – Cj

=      206575518 + 146979576.2 – 157573862        –         188955653.5

=      7025578.7

ANOVA TABLE

SV	d.f	S.S	M.S
Constant (m) Age – Group  (ai) Item (bj) Error	1 4 3 12	146979576.2 10594285.8 41976077.3 7025578.7	2648571.45 13992029.77 585464.89
Tj	20	206575518

 

sF – ratio

4.52

23.90

Conclusion:

Since the calculated value is greater than the table value we reject H₀ and conclude that the average spending of students from various age-group is not same.  And also since the calculated value is greater than the table value we reject H₀ and conclude that average expenditure of students and items are not the same.