Solution Of Assignment No.2 (Course STA301) Fall 2012

Solution Of Assignment No.2 (Course STA301) Fall 2012 

Question 1: 

A)The fourth mean moment of a symmetric distribution is 243. What would be the value of the standard deviation in order that the distribution may be meso-kurtic?

SOLUTION:-

Standard is equal to 2nd moment
We are that m4 = 243 . Therefore
m4 = 243
m4/m2 = b3 = 3  i.e   = 243/m2^2 = 3
or 243/3 = 81 or m2 = 9
Standard deviation is equal to m  2nd moment


B)Two candidates X and Y at the B.A (Hons.) Examination obtained the following data.

Candidate X Candidate Y   
 = 43.2 =        20.5   
S.D = 24.25   S.D = 15.6  
Which of the candidate showed a more consistent performance?
SOLUTION:-
By calculating the co-efficient of variation in each case.

Candidate A

C V = s/x * 100
C V = 24.25/43.2 * 100
C V = 56.13%

Candidate B

C V = s/y * 100
C V = 15.6/20.5*100
C V = 76.097%

We see that co­efficient of variation for the candidate A smaller than that for the
candidate B.Hence candidate A is more consistent than candidate B

Question 2:

A)If coefficient of skewness = 0, then what would you say about the shape of the distribution?

SOLUTION:-

For symmetric distributions or curves, the coefficient is zero. The shape is symmetric

B)The following data were computed from personnel records of a manufacturing firm:
             X = Number of years of service
            Y = weekly wage rate
          n = 23; ∑X = 2433; ∑Y = 4254, ∑   = 281019;   = 841786 and  = 482788
 If the correlation coefficient indicates that there does exist a relationship between X and Y,                                    compute the least squares line of regression Y = a + b X. 
SOLUTION:-
Where bxy = n (XY)-(X)(Y) / n (X^2)-(X)^2

bxy = 23(482788) (2433)(4254) / 23(281019) (2433)^2
bxy = 11104124-10349982 / 6463437-5919489
bxy = 754142/543948
b     = 1.3864
a     = y-bx

y   = ￥y/n = 

4254/23 = 

184.96

x  = 

￥x/n = 

2433/23 = 105.78

a = 184.96-1.39(105.78)

a = 184.96-147.0342

a = 37.92

Hence

y  = 37.92+1.39X

Is estimated regression equation appropriate for predicting the no

of years (x) given weekly wage rate