Punjabi University 2008 B.Com Statistical Techniques - Question Paper

B.Com Statistical Techniques Paper - IV ques. paper

Time : three Hours] [Total Marks : 70


Instructions : (1) Figures on the right side indicate marks of every ques.. (2) Use of simple calculator and statistical tables is allowed.



1. (a) describe Correlation. Derive the formula for Spearman’s Correlation Coefficient.
Also prove that –1 = r = 1. 7

(b) find the regression line of Y on X; find the estimated value of Y when
X = 50, from the data beneath : 7


X
48
49
50
51
52
53
54
55
56

Y
98
100
88
102
95
125
120
110
125

OR

(a) Prove that “Coefficient of Correlation is independent of change of Origin and
Scale”. 7
_ _
(b) obtain X , Y , r, bXY and bYX from the subsequent 2 equations : 7

(i) 3x – 4y + 24 = 0 (ii) 4x – y – 16 = 0


2. (a) find the regression formula of x1 on x2 and x3. 7

(i) If r12 = 0.86, r13 = 0.65, r23 = 0.72, obtain r12.3
(ii) If r12 = r13 = r23 = 0.5, obtain r12.3 and R1(23)





OR
r two + r 2



- two r r r

(a) In usual notations, prove that R1(23)

= 12 13 12 13 23 7
2





(b) If s1 = 3, s2 = 5, s3 = four and if A =


obtain the values of b12.3 and r12.3.



1
0.7
- 0.6

1 -

0.7
1
0.8

r23

- 0.6
0.8 7
1

3. (a) What is an estimator ? define the properties of a good estimator. 7

–? x

(b) find the maximum likelihood estimator of ? if f (x; ?) = e ?


, x = 0, 1, 2, … 7



OR

(a) discuss the subsequent terms : 8

(i) Null and Alternate hypotheses

(ii) Simple and Composite hypotheses

(iii) Level of significance and power of the test. (iv) Type-I and Type-III errors

(b) A coin is tossed five times. Probability of getting success is p. To test the hypothesis
1 3
H0 : p = two vs. H1 : p = four , if head is found more than 3 times, H0 is rejected.
obtain the probability of type-I and type-II errors. Also obtain the power of the test. 6



4.
(a) describe ?2-Statistic. define ?2-test for independence of 2 attributes.
7

(b)
Test the goodness of fit of Poisson Distribution to the subsequent data :
7


x
0
1
2
3
4
Total

f
122
60
15
2
1
200


OR



(a) In which circumstances Yates Correction is necessary in ?2-test ? discuss this
correction with illustration. 7
(b) The subsequent data are found from a sample survey of adult males of four
cities : 7



Marital Status
City

A
B
C
D

Married
137
164
152
147

Unmarried
32
57
56
35

Test whether no. of adult males in cities and marital status are independent.


5. (a) elaborate Non-parametric tests ? How do they differ from Parametric tests ?
discuss in detail Run test. 8
(b) 2 various fertilizers were used to a sample of 8 plots of identical size every.
The farm yield from these plots are provided beneath : 6


Plot No.
1
2
3
4
5
6
7
8

Fertilizer A
49
32
44
48
51
34
30
42

Fertilizer B
40
45
50
43
37
47
55
57

The researcher would like to test the hypothesis that the 2 fertilizers yield the
identical median output. Test the hypothesis at five percent level of significance.

OR

(a) Suppose we want to compare the mean lifetimes of 2 types of 9-volt batteries on the basis of the subsequent life time (in hours) :


Brand A : 6.9, 11.2, 14.0, 13.2, 9.1, 13.9, 16.1, 9.3, 2.4, 6.4, 18.0, 11.5


Brand B : 15.5, 11.1, 16.0, 15.8, 18.2, 13.7, 18.3, 9.0, 17.2, 17.8, 13.0, 15.1

Using Mann-Whitney’s U-test, test the hypothesis that there is no difference in the mean lifetime of the 2 types of batteries at five percent level of significance. 7

(b) In the data below, X represents 10 scores of members of a control group in an experiment, Y represents the scores of 10 matched individuals who were provided the identical test. Test the hypothesis of no difference using Wilkoxon Matched-Pairs Sign-rank test at 5% level of significance : 7


X :
46
68
60
58
42
43
40
56
38
58

Y :
36
50
58
40
44
43
29
36
46
48

Earning:   Approval pending.