Quantitative Analysis Assignment
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BANGALORE MANAGEMENT ACADEMY
QAF ASSIGNMENT NO. 2 USE OF STATISTICAL TOOL FOR ANALYSIS OF DATA
SUBMITTED TO MR. MOHANASUNDARAM SUBMITTED BY PETHE SARANG SUNIL BLR0907033052
QAF ASSIGNMENT NO. 2 USE OF STATISTICAL TOOLS FOR ANALYSIS OF DATA In the present study I am using combined budgetary transactions of centre and states in rural development and roads & bridges as data; the data is taken from year 1998 to 2007. I am using mean and median for measure of central tendencies. We are using standard deviation and correlation coefficient for measure of dispersion. We are using scatter diagram and bar diagram for diagrammatic representation. The mean value of expenditure in rural development is Rs. 26973.732 crores while the mean value of expenditure in roads and bridges is Rs. 27962.092 crores. This shows that the average expenditure in roads and bridges is greater than that of rural development. The median value for expenditure in rural development is Rs. 24725.42 crores while the median value of expenditure in roads and development is Rs. 22296.265 crores. Then we have found the correlation coefficient, the correlation coefficient is found out to be 0.9759. The scatter diagram is also drawn, from the correlation coefficient and scatter diagram we find that expenditure in rural development and roads & bridges is perfectly positively correlated. This shows that the expenditure in rural development and roads & bridges is highly correlated. I have then used bar diagram to show the expenditure in rural development and roads & bridges from 1998 to 2007. From this bar diagram we can see that the expenditure in rural development is more than roads & bridges for first seven years. For the next three years the expenditure on roads & bridges is more. This shows that from year 1998 to 2004, the government has spent more on rural development and development of rural areas was the main objective. In later years more spending was done of building roads and bridges. In the inferential statistics part, we are using testing of hypothesis to find out whether the budgetary transaction on rural development is superior to roads and bridges. I have used here difference in mean and t test as the sample size is less than 30. The calculation is shown in annexure. I have found that budgetary expenditure on rural development is not superior to roads and development.
FORMULAE & CALCULATIONS PETHE SARANG SUNIL BLR0907033052
Page 2
QAF ASSIGNMENT NO. 2 Here consider, Rural development =X and Roads and bridges=Y
Measure of central tendency and dispersion. mean =
∑X N
Solution:
= 26973.732 AND X
= 27962.092 Y
n n ( )value + ( + 1)value 2 median = 2 2 Solution: Median value of X = 24725.42 and Median value of Y = 22296.265
∑(X − X )
2
σ=
n
Solution:
12245.6114 and
σy =
σx =
r=
15474.763
∑ ( X − X )(Y − Y ) ∑ ( X − X ) ∑ (Y − Y ) 2
2
Solution: r = 0.9759 this shows that expenditure on rural development and roads & bridges are perfectly positively correlated. PETHE SARANG SUNIL BLR0907033052
Page 3
QAF ASSIGNMENT NO. 2
Diagrammatic representation
Budgetary expenditure on rural development and roads & bridges
Scatter diagram representation
Testing of hypothesis Here I am going to test following hypothesis “is budgetary expenditure on rural development superior than roads and bridges” So here the null hypothesis is as follows, H0: budgetary expenditure on rural development is not superior to roads and bridges Alternate hypothesis will be, H1: budgetary expenditure on rural development is superior to road and bridges. Here as the sample size is less than 30 i.e. n < 30 so I am using ‘t’ test for difference in mean.
t=
X1 − X 2 1 1 S − n1 n2
PETHE SARANG SUNIL BLR0907033052
Page 4
QAF ASSIGNMENT NO. 2 (n1 − 1) s12 + (n2 − 1) s2 2 S= n1 + n2 − 2 Solution: S = 13953. Here
= 15474.763,
= 12245.6114, s1
n1 = n2
s2
= 26973.732 and
X1
= 10
= 27962.092
X2
Therefore,
= 0.1584 tcal
ttab = tn1 +n 2 − 2df
= 2.552 ttab Now, as
> ttab
we accept H0. tcal
Thus our hypothesis we accept null hypothesis. This shows that budgetary expenditure on rural development is not superior to expenditure on roads and bridges.
PETHE SARANG SUNIL BLR0907033052
Page 5
QAF ASSIGNMENT NO. 2
ANNEXURE DATA YEA R 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
RURAL ROADS DEVELOPMENT 15474.91 16129.81 14728.89 17981.46 23111.59 26339.25 26522.84 36767.78 44416.38 48264.41
AND
BRIDGES 10990.87 15086.74 19373.51 19351.68 22054.79 22537.74 23932.84 38539.16 50881.64 56871.95
Source: finmin.nic.in
PETHE SARANG SUNIL BLR0907033052
Page 6
QAF ASSIGNMENT NO. 2 USE OF STATISTICAL TOOL FOR ANALYSIS OF DATA
SUBMITTED TO MR. MOHANASUNDARAM SUBMITTED BY PETHE SARANG SUNIL BLR0907033052
QAF ASSIGNMENT NO. 2 USE OF STATISTICAL TOOLS FOR ANALYSIS OF DATA In the present study I am using combined budgetary transactions of centre and states in rural development and roads & bridges as data; the data is taken from year 1998 to 2007. I am using mean and median for measure of central tendencies. We are using standard deviation and correlation coefficient for measure of dispersion. We are using scatter diagram and bar diagram for diagrammatic representation. The mean value of expenditure in rural development is Rs. 26973.732 crores while the mean value of expenditure in roads and bridges is Rs. 27962.092 crores. This shows that the average expenditure in roads and bridges is greater than that of rural development. The median value for expenditure in rural development is Rs. 24725.42 crores while the median value of expenditure in roads and development is Rs. 22296.265 crores. Then we have found the correlation coefficient, the correlation coefficient is found out to be 0.9759. The scatter diagram is also drawn, from the correlation coefficient and scatter diagram we find that expenditure in rural development and roads & bridges is perfectly positively correlated. This shows that the expenditure in rural development and roads & bridges is highly correlated. I have then used bar diagram to show the expenditure in rural development and roads & bridges from 1998 to 2007. From this bar diagram we can see that the expenditure in rural development is more than roads & bridges for first seven years. For the next three years the expenditure on roads & bridges is more. This shows that from year 1998 to 2004, the government has spent more on rural development and development of rural areas was the main objective. In later years more spending was done of building roads and bridges. In the inferential statistics part, we are using testing of hypothesis to find out whether the budgetary transaction on rural development is superior to roads and bridges. I have used here difference in mean and t test as the sample size is less than 30. The calculation is shown in annexure. I have found that budgetary expenditure on rural development is not superior to roads and development.
FORMULAE & CALCULATIONS PETHE SARANG SUNIL BLR0907033052
Page 2
QAF ASSIGNMENT NO. 2 Here consider, Rural development =X and Roads and bridges=Y
Measure of central tendency and dispersion. mean =
∑X N
Solution:
= 26973.732 AND X
= 27962.092 Y
n n ( )value + ( + 1)value 2 median = 2 2 Solution: Median value of X = 24725.42 and Median value of Y = 22296.265
∑(X − X )
2
σ=
n
Solution:
12245.6114 and
σy =
σx =
r=
15474.763
∑ ( X − X )(Y − Y ) ∑ ( X − X ) ∑ (Y − Y ) 2
2
Solution: r = 0.9759 this shows that expenditure on rural development and roads & bridges are perfectly positively correlated. PETHE SARANG SUNIL BLR0907033052
Page 3
QAF ASSIGNMENT NO. 2
Diagrammatic representation
Budgetary expenditure on rural development and roads & bridges
Scatter diagram representation
Testing of hypothesis Here I am going to test following hypothesis “is budgetary expenditure on rural development superior than roads and bridges” So here the null hypothesis is as follows, H0: budgetary expenditure on rural development is not superior to roads and bridges Alternate hypothesis will be, H1: budgetary expenditure on rural development is superior to road and bridges. Here as the sample size is less than 30 i.e. n < 30 so I am using ‘t’ test for difference in mean.
t=
X1 − X 2 1 1 S − n1 n2
PETHE SARANG SUNIL BLR0907033052
Page 4
QAF ASSIGNMENT NO. 2 (n1 − 1) s12 + (n2 − 1) s2 2 S= n1 + n2 − 2 Solution: S = 13953. Here
= 15474.763,
= 12245.6114, s1
n1 = n2
s2
= 26973.732 and
X1
= 10
= 27962.092
X2
Therefore,
= 0.1584 tcal
ttab = tn1 +n 2 − 2df
= 2.552 ttab Now, as
> ttab
we accept H0. tcal
Thus our hypothesis we accept null hypothesis. This shows that budgetary expenditure on rural development is not superior to expenditure on roads and bridges.
PETHE SARANG SUNIL BLR0907033052
Page 5
QAF ASSIGNMENT NO. 2
ANNEXURE DATA YEA R 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
RURAL ROADS DEVELOPMENT 15474.91 16129.81 14728.89 17981.46 23111.59 26339.25 26522.84 36767.78 44416.38 48264.41
AND
BRIDGES 10990.87 15086.74 19373.51 19351.68 22054.79 22537.74 23932.84 38539.16 50881.64 56871.95
Source: finmin.nic.in
PETHE SARANG SUNIL BLR0907033052
Page 6
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