Gujarat University 2005 B.Com Third Year - Question Paper
TC-11
Statistical Techniques
Paper - IV
Seat No :
Statistical Techniques Paper - IV
Time : 3 Hours] [Total Marks : 70
: (1) Wsll Udl yo -o u?ddl oj. - lR A.
(2) &l- oik4i .H'tf ylouH o1o1 ciiniciidfl_ A.
1. (y) cii'oii yinll. Rnilddl -HHlo. ilc|l. ii[ii o\
0 -1 < r < 1. 7
(l) ill[ll GnR?ll Y dl x 5-lC-l nR-fl, [l0lliifel olldj, ol icll .H'tf
X = 50 -Vi cll. Y dl yl0l[ld [0ill ilcll : 7
|
X |
48 |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
|
Y |
98 |
100 |
88 |
102 |
95 |
125 |
120 |
110 |
125 |
(y) ll[ld o\0 &-.:hMo omM- yd, t-ldl ufcclld?ll A. 7
(l) dMdl ifto l\ X , Y , r, bXY y-l bYX iml : 7
(i) 3x - 4y + 24 = 0
(ii) 4x - y - 16 = 0
2. (y) x1 di x2 yd. x3 nRd! [ddH .lldl ftHlol ilcl\. 7
(ii) r12 = r13 = r23 = 0.5 -Vi d\ r12 3 y-l R3) SllHl.
ywi
2 2
2. (yl) U?l[ld l0 Hill lfod o\0 : r1(23) = r12 + *13 - 22r12 r13 r23 7
1 - r23
3. (y) yioisio yC-i ?j. ? yo &RI yl0ll0dtl opum ftHmcU.
7
7
(i) f (x ; X) = , x = 0, 1, 2, ... -k ll X -ll h-tih (Mimi ylollo
(y) HMdi nl-l ll'lclt : 8
(i) [dRlostk yd <0 [nto ufcoeLKl
(ii) *11-1 ydl Pl$i UfcoeiKl
(iii) lllo Udd on yd. uhUiSldj l
(iv) nlll yd nlo rHI c-ii
(i) yo [&&1 5 qxl (3AmiHi yicj A. AW. H VO, *bimi p A. H0 : p = 1 [<6 3
H1 : p = 4 dl Hft&Sl ocji l 3 all cjfej cjii AW. H ii H0 Hi cftoiq. o ini yicj A. uih yd uorHI c-ilHl mi ydj Hftwsidi i ilU. 6
4. (y) x2-yjoiiod{l cjiii yinji. i oijfcili dll cjliii iiidj x2-njhlil cjjcll. (i) HMHl Hl[-il Hl utoi. ftxRKl ywLH i.o0jii injiil :
7
7
|
x |
0 |
1 |
2 |
3 |
4 |
o Cj NO |
|
f |
122 |
60 |
15 |
2 |
1 |
200 |
(l) =MR ?l-3.Hl U'H! yMi dM i$t A. 7
|
?l-h | ||||
|
CPd [yiCrl |
A |
B |
C |
D |
|
ClOdi o Cii |
137 |
164 |
152 |
147 |
|
O q.Rl NO |
32 |
57 |
56 |
35 |
'g-l 'g-l SLMhL niM nilid-H l yd. .Hd! C-LO [?i[l 4o H'L?il [dR A
O d-l i inilil.
5. (y) yURC-lk u3kl yCl ? i uiaieth u3k.SlM O hli -i A ? yilH u3kl (Run test) PtfriRll ymd. 8 (i) yiHld iini ciil 8 'ft'Mldl ir. l $-L HURl -d yiuq.LHl yk A. yi 'ft'Mldl nRil HCd Gwi A : 6
|
nll d. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Hl-R A |
49 |
32 |
44 |
48 |
51 |
34 |
30 |
42 |
|
Hl-R B |
40 |
45 |
50 |
43 |
37 |
47 |
55 |
57 |
yMHOlA dnilici A O &M. Hld iiidt Hiii GrU-ld yini A. yi 'M.R.OC-Mi 5% dll yuO-ill oiiy dUiyl.
(y) 9-cilCd{l l UORdl .&yidl yiUl cMyin dl yRHLHll dMAl ii[.il Ull ocil A :
|
UdS 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 |
|
UdS 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 |
5% dl yu2ioriHl o $u.y Mann-Whitney dl U-u3k.SHl Qnioi o 6(4 UORd! .&yidl yiH0_ yiHK AO On. iyl. 7
|
(i) HlaHl iLCrdil X 4 4= ..-41 10 G4.[drL4\ iL 4= UHlon.L [d.HiSL ft -SlR $. Y 10 c0[OrL4l.dLL 4 ylom o{L - SlR $. Wilkoxon dl lilyl ilMl Lflll-ilo u3k.SL dll Qnllol o& dcidd! ll%{o{l mM, u3k.SL ll Modl-l oftl 5% M. 7 | ||||||||||||||||||||||
|
Statistical Techniques Paper - IV
Time : 3 Hours] [Total Marks : 70
Instructions : (1) Figures on the right side indicate marks of each question.
(2) Use of simple calculator and statistical tables is allowed.
1. (a) Define Correlation. Derive the formula for Spearmans Correlation Coefficient.
Also prove that -1 < r < 1. 7
(b) Obtain the regression line of Y on X; obtain the estimated value of Y when X = 50, from the data below : 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) Find X , Y , r, bXY and bYX from the following two equations :
7
(i) 3x - 4y + 24 = 0
(ii) 4x - y - 16 = 0
(a) In usual notations, prove that R
7
(b) If a1 = 3, a2 = 5, a3 = 4 and if A
7
|
r12 + r123 - 2 r12 r13 r23 | |||||||||||||
|
1(23) |
| ||||||||||||
3. (a) What is an estimator ? Describe the properties of a good estimator. 7
e-X Xx
(b) Obtain the maximum likelihood estimator of X if f (x; X) = , x = 0, 1, 2, ... 7
OR
(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 5 times. Probability of getting success is p. To test the hypothesis
1 3
H0 : p = 2 vs. H1 : p = 4 , if head is obtained more than three times, H0 is rejected. Find the probability of type-I and type-II errors. Also find the power of the test. 6
4. (a) Define x1-Statistic. Describe x2-test for independence of two attributes. 7 (b) Test the goodness of fit of Poisson Distribution to the following 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 x2-test ? Explain this correction with illustration. 7
(b) The following data are obtained from a sample survey of adult males of four
cities : 7
| |||||||||||||||||||
|
Test whether no. of adult males in cities and marital status are independent. | |||||||||||||||||||
5. (a) What are Non-parametric tests ? How do they differ from Parametric tests ?
Explain in detail Run test. 8
(b) Two different fertilizers were used to a sample of eight plots of same size each. The farm yield from these plots are given below : 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 two fertilizers yield the same median output. Test the hypothesis at 5 percent level of significance.
(a) Suppose we want to compare the mean lifetimes of two kinds of 9-volt batteries on the basis of the following 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-Whitneys U-test, test the hypothesis that there is no difference in the mean lifetime of the two kinds of batteries at 5 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 given the same 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 |
TC-11 7 P.T.O.
(a) Obtain the regression equation of x1 on x2 and x3.
(b) (i) If r12 = 0.86, r13 = 0.65, r23 = 0.72, find r
(ii) If r12 = r13 = r23 = 0.5, find r12 3 and R1(23)
OR
|
Attachment: |
| Earning: Approval pending. |
