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Statistical Research Project MBA 2009-2012 ¦ BUSINESS STATISTICS

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Statistical Research Project

MBA 2009 - 2012

10/4/2009

Rajesh Kumar Garg

Ravi Ganesh

Saurabh Agarwala

Siddharth Sikka

Ujjwal Malik




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Table of Contents

Problem Statement ..........................................................................................................................................3

Background ......................................................................................................................................................3

Method ............................................................................................................................................................4

Results ..............................................................................................................................................................6

Conclusions ................................................................................................................................................... 14

Recommendations ........................................................................................................................................ 14References .................................................................................................................................................... 14




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Problem Statement

ABC HR Consultancy needs to set employee wages across different Industry sectors in a given geographical

area, for the coming year

Background

At the end of every year ABC HR Consultancy designs wages across sectors based on the Current

Population Survey data, for the coming year. The wage analysis is used to by the ABC HR Consultancy to

help its client benchmark their employee wages for the forthcoming year. This wage analysis is carried out

on this data. The wage analysis takes into account the dependency of wage on the following factors

Gender

Years of Experience

Sector

Occupation

The aim of the wage analysis is to determine the following:

1. Percentage distribution of jobs across genders , sectors occupation and years of experience

2. Mean wage and cumulative distribution for the population

3. Summary Statistics of wage across gender, sectors, occupation and years of experience

4. Modelling of wage against years of experience

5. Proving four results using hypothesis testing




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Method

The Current Population Survey (CPS) is used as the sample date for the wage analysis. This data consists

of a random sample of 534 persons from the CPS, with information on wages and including Gender, years

of work experience, sector and occupation

1. The sample data is sorted on the basis of the “wages”.

2. The population distribution analysis of the area is done based on the following:

o Gender distribution

o Sector

o Occupation

o Years of Experience (with appropriate intervals )

The results for this are highlighted in Section 1 of the “Results Section”

3. The descriptive statistics are carried out on the sample data including the 5-N summary. These consist

of :

o Minimum

o Maximum

o 1st Quartile

o 3rd

Quartile

o Median

o Mode

o Standard deviation

o Mean

o Cumulative Wages

o Kurtosis

o Variance

o Range, etc.

The results for the above are highlighted in Section 2 of the “Results Section”

4. Summary Statistics are created in form of Box-plots to analyse the wages across four different

parameter. The results for the above are highlighted in Section 3 of the “Results Section”

5. The wages are modelled against the “Years of Experience”. The results for the above are highlighted

in Section 4 of the “Results Section”

6. Hypothesis testing is utilized to carry out 4 different tests to prove the wage analysis across four

chosen areas




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Results

Section 1: A series of the pie-charts given below have been used to describe the percentage distribution

amongst the following parameters

1. Gender : The distribution of male and females working population in the geography is 54 % and

46 % respectively

2. Sector: More than Two-thirds of the Jobs in the area are concentrated in the non-

manufacturing and non-construction sectors

46%54%

Gender

Female Male

4%

19%

77%

Sector

Construction Manufacturing Others




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3. Occupation: “Other” category of options form the highest concentration of occupations in the

area, followed by “Professional” and “Sales” related occupat ions

4. Years of Experience: The distribution of the years of experience is almost evenly divided in the

geographical area amongst different sectors. This provides a insights into the strengths and

accuracy of the sample data

18%

10%

29%20%

7%

16%

Occupation profile

Clerical Management Others

Professional Sales Service

20%

19%

22%

18%

21%

Experience

0 to 6 yrs 7 to 12 yrs 13 to 18 yrs

19 to 28 yrs 29 plus yrs




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Section 2: This section makes use of descriptive statistics to provide a view of the mean and cumulative

wage

1. Mean Wage: The graph and the table below provide a view of the descriptive statistics. The

mean wage is $9 an hour with a standard

2. Cumulative Wage: The cumulative wage graph provides the view of the wages as distributed

over the complete sample population.

0

10

20

30

40

50

60

70

1 3 5 7 9 11 1 3 15 1 7 19 2 1 23 25 2 7 29 3 1 33 35 3 7 39 4 1 43 4 5

Number of people

Wage ($ per hour)

Mean

Statistic Valu e

Mean 9.0

Standard Error 0.2

Median 7.8

Mode 5.0

Standard Deviation 5.1

Sample Variance 26.4

Kurtosis 5.0

Skewness 1.7

Range 43.5

Minimum 1.0

Maximum 44.5

Sum 4818.9Count 534.0

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Cumulative Wage Distribution

Wage ($ per hour)




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Section 3: This section makes use of box plots to plot the wages against all the different parameters

including: Gender, Sectors, Occupations and Years of Experience

1. Summary statistics for the wages across genders and sectors

2. Summary statistics for the wages across Occupations

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

MALES

FEMALES

SECTOR : CONSTRUCTION

SECTOR : MANUFACTURING

SECTOR : OTHERS

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

OCCUPATION: CLERICAL

OCCUPATION : PROFESSIONALS

OCCUPATION : SALES

OCCUPATION : SERVICE

OCCUPATION: MANAGEMENT

OCCUPATION : OTHERS




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3. Summary statistics for the wages across years of experience

4. Summary statistics for the wages of the total population- It can be surmised that majority of

the population has wages lying between $5 - $11 an hour

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

TOTAL POPULATION

EXP : 0-6 yrs

EXP : 13-18 yrs

EXP : 19-28 yrs

EXP : 28+ yrs

EXP : 7-12 yrs

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48




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Section 4: In this section wage has been plotted against the Years of experience. The table attached with

the graph provides the best possible predication of wages with the least average error

Experience

W a g e




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Section 5: In this section we have surmised the results of four tests through Hypothesis testing

TEST 1

H0: Average wage of female employees is same as overall average

H1: Average wage of female employees is not equal to overall average

Type of test z test

x bar 7.9

mu 9.0

sigma 4.5

n 245.0

z value -3.5

Conclusion: H0 rejected with 99% confidence. There is a difference in average wage of females from the

overall average

TEST 2

H0: Average wage of employees in manufacturing sector is same as overall average

H1: Average wage of employees in manufacturing sector is not equal to overall average

Type of test z test

x bar 9.6mu 9.0

sigma 4.5

n 99.0

z value 1.1

Conclusion: H0 not rejected at even 90% confidence level. There is no difference in average wage of

manufacturing sector employees from the overall average




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TEST 3

Test whether variance in wage of management is higher, lower or equal to that of total sample

Sample Size 55 n

Sample Variance 57.34 s

2

Test Statistic 117.242

2

Null hypothesis p-value 1%

H02 =

26.41 0.0 Reject

H02

>=

26.41 1.0

H02 <= 26.41 0.0 Reject

Conclusion: Variance in wages of management is higher than that of total sample

TEST 4

H0: Proportion of females working in clerical / service sectors is greater than overall sample proportion by

not more than 10%

H1: Proportion of females working in clerical / service sectors is higher than overall sample proportion by

more than 10%

Type of test z test

Sample proportion 0.7

Population proportion 0.5n 180.0

z value 3.7

Conclusion: Null hypothesis is rejected. Proportion of females is greater than 10%




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Conclusions

Recommendations

References

Economics Web Institute - http://www.economicswebinstitute.org

http://www.economicswebinstitute.org/




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