Veer Narmad South Gujarat University 2011-3rd Year B.Com SB-0518 Statistics : ( - 3 ) . - Question Paper
Third Year B. Com. Examination March / April - 2011 Statistics : Paper - III
Time : 3 Hours] [Total Marks : 70
N Seat No.:
6silq<3i Puunkiufl SnwiA u* qsq <KH=fl. Fillup strictly the details of signs on your answer book.
Name of the Examination :
T. Y. B. Com.
Name of the Subject:
Statistics : Paper - 3
Student's Signature
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-Subject Code No.: |
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-Section No. (1,2......): Nil |
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|
3lUl(M |
A |
61(3*1 B |
C | |
|
X |
8 |
7 |
3 |
60 |
|
Y |
3 |
8 |
9 |
70 |
|
Z |
11 |
3 |
5 |
80 |
|
HR |
50 |
80 |
80 |
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(x-x)2 =135 HIM. d. faaRSl Hia 90%
(a) [HsIh fcltfiddl *1$ UM-il *10*11*1 H6t1H HUfetd 275
Hl d. 41M Hlfecft HVtt IR&d *iM EVPI Hiql.
|
HR |
15 |
16 |
17 |
18 |
19 |
|
HtLH <t0UR |
300 |
320 |
340 |
360 |
380 |
|
WHlHl |
0.15 |
0.25 |
0.40 |
0.15 |
0.05 |
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J = 48.5, X(x/_J) =240 ifo:lI = 50 Hl Htal IRSlM &Hd ?LlH\.
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|
A |
D2 |
D3 |
D4 | ||
|
<h |
42 |
48 |
38 |
37 |
160 |
|
o2 |
40 |
49 |
52 |
51 |
150 |
|
0.3 |
39 |
38 |
40 |
43 |
190 |
|
HR |
80 |
90 |
110 |
160 |
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M | ||||
|
hU* |
1 |
2 |
3 |
4 |
|
A |
60 |
40 |
60 |
70 |
|
B |
20 |
60 |
50 |
70 |
|
C |
20 |
30 |
40 |
60 |
|
D |
30 |
10 |
20 |
40 |
U) *1$ &Hld [1 HHl'gH dlldL \httti. Y
HqciciLHl aHL=HL d. &H[dl Hil Hld d. =*H Uk&mi
5% MKl H&SM S$L.
|
[dtrf-I |
[dL-II |
[dUL-III |
|
8 |
7 |
12 |
|
10 |
5 |
9 |
|
7 |
10 |
13 |
|
14 |
9 |
12 |
|
11 |
9 |
14 |
Y (*l) WR d A.H cHR <H Q.% OtdL Hil HMl Y
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?Hd 73 tk Ah dl &0Hil HC-iLlHL *di Sfell &. ?HH M ?1IH ?
OH*iR <LLcL & :
|
*m-i |
*m-2 | |
|
OimI ?. |
10 |
15 |
|
Hl& *R*l*l Hdd (3. Hi) |
440 |
460 |
|
40 |
45 |
<H &H[Hl Uml)dl fall &HK &. ?H Hl>K'H-lL UftWil
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|
$tl -> ARhSC-I I |
dlA |
*IH |
*i-H &>l |
5<y. VO |
|
X |
48 |
10 |
110 |
168 |
|
Y |
12 |
80 |
100 |
192 |
|
h&L VO |
60 |
90 |
210 |
360 |
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d *A 13 .OlHl Hia 0.278 &. <Hd
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|
HR (%LUHL) |
20 |
21 |
22 |
23 |
24 |
|
%i<HKdl |
0.1 |
0.2 |
0.3 |
0.3 |
0.1 |
(*l) &HI HliWl Hd H[l[ci HLLHl Vldl i*l.
(0 =lld* ili dHR i*l.
(3) di-Mld ili dHR i*l.
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|
(3tHlddl vftiR |
H!1 |
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*u*l |
80 |
70 |
50 |
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50 |
45 |
40 |
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hM |
-25 |
-10 |
0 |
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H*l<U
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*U<*U B HH rt UfcK-Udl U&SM %LsU S$L : | ||||||||||||||||||||
|
|
X |
14 |
17.4 |
15.6 |
8.2 |
13.8 |
15.4 |
16.3 |
17.7 |
15 |
13.4 |
|
Y |
18 |
16.3 |
13.3 |
15.8 |
18 |
20.4 |
15.7 |
21.5 |
14.5 |
16.7 |
|
X |
30.4 |
16 |
13.3 |
13.9 |
21.1 |
14.0 |
16.2 |
11.5 |
10.4 |
12.6 |
18.1 |
|
Y |
13.7 |
30.6 |
17.0 |
15.7 |
16.8 |
18.8 |
18.8 |
16.0 |
14.6 |
12.3 |
17.1 |
(2) Figures to the right indicate full marks.
(3) Statistical tables and graph papers will be provided on request.
(4) Simple calculator can be used.
Answer the following questions :
10
(1) Find the solution of following transportation problem by Matrix Minima method :
|
Origins |
A |
Destinations B |
C |
Supply |
|
X |
8 |
7 |
3 |
60 |
|
Y |
3 |
8 |
9 |
70 |
|
Z |
11 |
3 |
5 |
80 |
|
Demand |
50 |
80 |
80 |
(2) A random sample of size 16 is taken from normal population gives J = 41, (x-x)2=135. Find 90% confidential limits for population variance.
(3) During the study of a problem of decision theory, maximum value of EMV is 275. According to usual notation, obtain the value of EVPI from the following data :
|
Demand |
15 |
16 |
17 |
18 |
19 |
|
Maximum Payoff |
300 |
320 |
340 |
360 |
380 |
|
Probability |
0.15 |
0.25 |
0.40 |
0.15 |
0.05 |
(4) A random sample Xj, x2,..x16 is taken from Normal
population gives J = 48.5, X(x/'-*) = 240. Find the
value of statistics for hypothesis HQ : |i = 50.
(5) A random sample of size 8 taken from the population is given below :
19, 18, 11, 9, 13, 15, 17, 13
Test the hypothesis that 'the population median is 12'.
2 (a) Explain the following terms : 6
(1) Constraints
(2) Objective function
(3) Basic solution
(b) Find the minimum and maximum values of the 6
objective function Z = xl+x2 from the following inequalities :
2xj + x2 > 4
3xj + 5x2 < 20
Xj - 3x2 < 2
2 (a) What is Linear programming ? Give its 4
mathematical formulation.
(b) A firm produces two types of tablets for Headache. 8 Each tablet of type A contain 2 Grain Aspirin, 5 Grain Bicarbonate and 1 Grain Codin. While each tablet of type B contain 1 Grain Aspirin, 8 Grain Bicarbonate and 6 Grain Codin. It could known that it is necessary to take minimum 12 Grain Aspirin, 74 Grain Bicarbonate and 24 Grain Codin to get immediate relief from Headache. Find out by Graphical method, how many tablets of both the types should be taken minimum to get quick relief from Headache ?
3 (a) Explain the Min. (Min-Max.) and Max (Min-Max) 4
method to find initial feasible solution of transportation problem.
(b) Intra Action Jute Ltd. is a leading firm in jute 8
industry. It wanted to fulfill the requirement of its own four regional depots. Following matrix shows the distance in kilometer from origin to destinations :
Destination
|
Origins |
Dl |
d2 |
D3 |
da |
Supply |
|
42 |
48 |
38 |
37 |
160 | |
|
o2 |
40 |
49 |
52 |
51 |
150 |
|
3 |
39 |
38 |
40 |
43 |
190 |
|
Demand |
80 |
90 |
110 |
160 |
Find the optimum programme to minimize the total transportation distance. Use Vogel's Approximation method to find out initial basic feasible solution.
OR
10
3 (a) Explain the Hungarian's method to find out the 4
solution of Assignment problem.
(b) Following data show the relative rating (100-best 4
rating) regarding the ability of four professors to teach the four courses. Assign each professor to the courses with a view to maximize educational quality.
|
Courses | ||||
|
Professors |
1 |
2 |
3 |
4 |
|
A |
60 |
40 |
60 |
70 |
|
B |
20 |
60 |
50 |
70 |
|
C |
20 |
30 |
40 |
60 |
|
D |
30 |
10 |
20 |
40 |
(c) Three samples are taken from Normal population 4
with equal variance. Test the hypothesis that the population means are equal at 5% levels of significance.
|
Sample-I |
Sample-II |
Sample-Ill |
|
8 |
7 |
12 |
|
10 |
5 |
9 |
|
7 |
10 |
13 |
|
14 |
9 |
12 |
|
11 |
9 |
14 |
4 (a) How will you test the significance of the difference 4 between two small sample means when samples are not in pair ? State your assumptions.
(b) The height of 6 seamen are 63, 65, 68, 69, 71 and 4 72 inches respectively while the height of 10 soldiers
are 61, 62, 65, 66, 69, 70, 71, 72, 69 and 73 inches respectively. Can you say that the soldiers are taller than the seamen ?
(c) Following are the data regarding random samples 4 of government employees of two states of India.
State-1 State-2
Sample size 10 15
Monthly average wages
(in 440 460
Sample variance 40 45
Test the hypothesis that 'the variances of two populations (states) are equal'.
OR
4 (a) Define y2 statistics. State its applications and 4
limitations.
(b) Can you say from the following data that the people 4 suffering from different dieseases, select the hospitals according to their dieseases ?
|
Diesease Hospitals -I |
Fever |
Tuberculosis |
Other dieseases |
Total |
|
X |
48 |
10 |
110 |
168 |
|
Y |
12 |
80 |
100 |
192 |
|
Total |
60 |
90 |
210 |
360 |
(c) Correlation coefficient between the length and bridth 4 of the head of 10 Brahmins is 0.324 and that of 13 Kshatriya is 0.278. Test the significance of difference between two correlation coefficients.
5 (a) Clarify the difference between the following terms : 4
(1) Maxmin and Maxmax criterian
(2) Expected Opportunity Loss (EOL) and Expected Value of Perfect Information (EVPI)
(b) A baker makes a type of Pastry at night and sales 8 it at daytime. As it is perishable, he throw away the unsold pastry. The cost of a pastry is ? 1 and its selling price is ? 3. The distribution of pastry's demand is as follows :
|
Demand (in numbers) |
20 |
21 |
22 |
23 |
24 |
|
Probability |
0.1 |
0.2 |
0.3 |
0.3 |
0.1 |
(1) Create the course of Action and states of nature
(2) Prepare the payoff matrix
(3) Prepare the opportunity loss table.
(4) Find EPPI, EMV and EVPI.
5 (a) Explain following terms : 6
(1) Pay-off matrix
(2) Hurwiczg's rule
(3) Baye's theorem.
(b) A toy manufacturing company introducing a new type 6 of a toy in the market. The company has to decide whether the production the toys is to be done at full level, partial or less. There are three levels of the acceptance of their product. The aspected conditional profit of the first year is as follows :
|
Acceptance of |
Profit (in |
o o p | |
|
product |
Full |
Partial |
Less |
|
Very good |
80 |
70 |
50 |
|
Average |
50 |
45 |
40 |
|
Below Average |
-25 |
-10 |
0 |
Take the optimum decision under the following rules :
(1) Laplas rule
(2) Hurwiczg rule
(3) Minmax rule
6 (a) Explain non-parametric Wilcoxen test. 4
(b) Following are two samples taken from same 8
population. Test that hypothesis at 5% level of significance using Mann Whitney test :
|
X |
2.3 |
2.4 |
2.4 |
2.5 |
2.7 |
2.9 |
2.9 |
|
Y |
2.6 |
2.8 |
3.0 |
3.1 |
3.1 |
3.2 |
3.2 |
14
6 (a) What is non-parametric test ? Explain the scales 4
methods using in it.
(b) Test the hypothesis that the following two samples 8 are taken from the same population, by using Sign test.
|
X |
13.3 |
14.6 |
13.6 |
17.2 |
14.1 |
10.6 |
15.9 |
14.7 |
14.2 |
|
Y |
14.1 |
15.1 |
9.9 |
14.5 |
17.9 |
16.1 |
16.8 |
15.1 |
13.2 |
|
X |
14 |
17.4 |
15.6 |
8.2 |
13.8 |
15.4 |
16.3 |
17.7 |
15 |
13.4 |
|
Y |
18 |
16.3 |
13.3 |
15.8 |
18 |
20.4 |
15.7 |
21.5 |
14.5 |
16.7 |
|
X |
30.4 |
16 |
13.3 |
13.9 |
21.1 |
14.0 |
16.2 |
11.5 |
10.4 |
12.6 |
18.1 |
|
Y |
13.7 |
30.6 |
17.0 |
15.7 |
16.8 |
18.8 |
18.8 |
16.0 |
14.6 |
12.3 |
17.1 |
SB-0518] 15 [ 6000 ]
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Attachment: |
| Earning: Approval pending. |
