N–1000
Seat No. ______
M. Ed. Examination April / May – 2003
Statistical Methods (New Course) Time : 3 Hours]
çñÇÞë Ñ
[Total Marks : 100
(1) fÞù KÝëÞÕñäýÀ äë_Çù ±Þõ µkëßù ÇùÀçë´ÕñäýÀ áÂù. (2) ØßõÀ ìäÛëÃÞë µkëßù ±áÃ-±áà µkëßäèíÜë_ áÂù. (3) ÖÜõ çëØð_ ÀõS@ÝðáõËß äëÕßí åÀù Èù.
ìäÛëà 1 1
(±) ±Þõ (Ú)Þë µkëß áÂù. IÝõÀ µkëß ±ëåßõ 750 åOØùÜë_ áÂù Ñ 15 (±) ç_ÃíÖ VÕÔëýÞë 10 VÕÔýÀùÞõ 3 ìÞHëëýÝÀù±õ ±ëÕõá ¿Ü ÞíÇõ ÜëHëõ Èõ. ±ëÕõáë ¿ÜÞë ±ëÔëßõ ¿Üë_À ÖÎëäÖ Õ©ìÖ×í ØßõÀ ½õÍí ÜëËõ γ ÃHëù. ÀÝë Úõ ìÞHëëýÝÀùÞí ½õÍíÞð_ ¿Üë_ÀÞ çú×í äÔð Þ°À Èõ Öõ Þyí Àßù Ñ
ìÞHëëýÝÀ Ñ I 1 7 5 10 3 2 4 9 6 8 ìÞHëëýÝÀ Ñ II 3 5 8 4 7 10 2 1 6 9 ìÞHëëýÝÀ Ñ III 6 4 8 9 1 2 3 10 5 7 ±×äë (±) ÇßHë M²×yßHëÞí ìäÛëäÞë çܽäù. ÖõÞë µÕÝùÃÞí ÕñäýÔëßHëë±ù À´ À´ Èõ ? ÞíÇõ hëHë Éñ×Þë 10 ìäzë×a±ùÞë ëMÖë_À ±ëMÝë Èõ ±ëÕõá ìäÃÖ Õß×í F ÜñSÝ åùÔí ±×ýCëËÞ Àßù Ñ
15
Éñ× A 13 11 12 12 9 11 8 10 11 7 Éñ× B 15 9 20 16 11 12 14 13 10 13 Éñ× C 9 12 14 10 8 6 7 9 8 11 N–1000]
1
[Contd...
(Ú) ÞíÇõÞí ÜëìèÖí Õß×í ±ëç_à çèç_Ú_Ôë_À ÃHëù Ñ
A B 15
35 65
I
30
20 55
II
40
10 50
III
45
5 15
IV
çëÜëìÉÀ VÖß
C
±×äë (Ú) çèç_Ú_Ôë_À ÃHëäëÞí ÕìßÚâ ÃðHëëÀëß Õ©ìÖÞí ç_ÀSÕÞë VÕWË Àßù. ±ë Õ©ìÖ äÍõ ÞíÇõÞí ÜëìèÖí Õß×í ÃìHëÖ ±Þõ ìäiëëÞÞë ëMÖë_Àù äEÇõÞù çèç_Ú_Ôë_À ÃHëí ÖõÞð_ ±×ýCëËÞ Àßù Ñ
ÃìHëÖ 66 72 55 82 69 75 89 59 46 62 ìäiëëÞ 53 68 49 73 56 65 74 71 58 56 ÞíÇõÞë ÕöÀí ÃÜõ Öõ Õë_ÇÞë µkëß áÂù. ØßõÀ µkëß ±ëåßõ 125 åOØùÜë_ áÂù Ñ (À)
ìäwÕÖë ±õËáõ åð_ ? ±õÀ ±ëT²ìkë ìäVÖßHë ÜëËõ ÜKÝV× = 69.03, P90 = 78. 72 ±Þõ P10 = 43. 69 èùÝ Öù ÖõÞí ìäwÕÖë ÃHëí ÖõÞù Àëß Þyí Àßù.
(Â) ½õ çèç_Ú_Ôë_À r = 0. 73 èùÝ Öù ç_¿ÜHë ±_À ÖõÜÉ ÕñäëýÞðÜëÞ ØåÖë±_À ÃHëù. (Ã) çÜÔëßHë ä¿Þí Õë_Ç áëZëìHëÀÖë±ù ÉHëëäù. (Cë) ½õ x1, x2 ±Þõ x3 hëHë Çáù èùÝ ±Þõ r12 = 0. 26 , r23 = 0. 28 ±Þõ r31 = 0.54 èùÝ Öù r12.3 Þð_ ÜñSÝ åùÔù.
(Ç) ÞíÇõÞë ÕëìßÛëìæÀ åOØù çܽäù Ñ (1) ìärëç çíÜë±ù (2) çë×ýÀÖëÞí ÀZëë±ù (3) åõÝÍóÞù çðÔëßù (4) ìÞßëÀßHëíÝ ÕìßÀSÕÞë. (È) ±äÝä M²×yßHëÞë µÕÝùÃùÞí ÝëØí Àßù ±Þõ ±õÀÞí çÜÉ ±ëÕù. 2
15
15
20
[Contd...
(É) µIÀSÕÞëÞí ÇÀëçHëí ÜëËõ ±õÀ ÕðEÈí ±Þõ ì¦ÕðEÈí ÀçùËí çܽäù. N–1000]
2
ìçì© ÀZëë
ìäÛëà 2 3
ÞíÇõÞë ÕöÀí ÃÜõ Öõ ÚõÞë µkëß áÂù. IÝõÀ µkëß ±ëåßõ 400 åOØùÜë_ áÂù Ñ (À)
20
ÞíÇõÞí ÜëìèÖíÞõ ±ëÔëßõ ÇÖðWÀùìËÀ çèç_Ú_Ô ÃHëí ÖõÞù 05, 01 ÀZëë±õ ìärëç ±_Ößëá ÃHëù Ñ Çá x ±çÎâ
çÎâ
Çá çðçÜëÝùìÉÖ
35
45
±çÜëÝùìÉÖ
30
15
y
(Â) ÀëÇë ëMÖë_ÀùÞõ ÜëHëÛñÖ ëMÖë_ÀÜë_ wÕë_ÖìßÖ ÀßäëÞë ÎëÝØë ÉHëëäù. ÞíÇõÞë ëMÖë_ÀùÞð_ σ Ö×ë z ëMÖë_ÀÜë_ wÕë_Öß Àßù Ñ (M = 60, S.D. = 6.3) 53, 41, 45, 64, 59
(Ã) ÞíÇõÞí ÜëìèÖí Õß×í ëMÖë_À VäwÕÜë_ ìÞÝÖç_Ú_Ô çÜíÀßHëù Üõâäù Ñ
ÃìHëÖ ìäiëëÞ ÀçùËí ÀçùËí çßëçßí . ìä.
X 50
Y 40
14
17
rxy = 0. 70
Ãúßäõ ÃìHëÖÜë_ 45 ÃðHë ÜõâTÝë èùÝ Öù ìäiëëÞÞë ç_ÛìäÖ ÃðHëÞð_ ±ÞðÜëÞ Àßù. 4
ÞíÇõÞë ÕöÀí ÃÜõ Öõ Õë_ÇÞë µkëß áÂù. IÝõÀ µkëß ±ëåßõ 150 åOØùÜë_ áÂù Ñ (À)
30
ÞíÇõÞë ëMÖë_ÀùÞð_ ÜëìHëÖ ìäÇáÞ ÃHëù Ñ 35, 51, 47, 32, 55, 43, 41, 62, 39
(Â) ÀáÜ M²×yßHë ±õËáõ åð_ ? ÖõÞð_ Üèkä ÉHëëäù. N–1000]
3
[Contd...
(Ã) ÇÖð×ýÀ ìäÇáÞ åùÔäë ÜëËõÞë_ çñhëù áÂí ÖõÜë_ äÕßëÝõáë ç_ÀõÖù VÕWË Àßù. (Cë) 40 ÀáÜùÞí ±õÀ ÀçùËíÞù ìärçÞíÝÖë ±_À ìärçÞíÝÖë ±_À ÀõËáù ×åõ, ½õ
0.55
Èõ. ÀçùËíÞù
(1) ÀáÜùÞí ç_AÝë äÔëßíÞõ 80 ÀßäëÜë_ ±ëäõ Öù ? (2) ÀáÜùÞí ç_AÝë äÔëßíÞõ 120 ÀßäëÜë_ ±ëäõ Öù ? (Ç) 80 ìäzë×a±ùÞë äÃýÜë_ ÃìHëÖ ìäæÝÜë_ çðìÞáÞù ¿Üë_À 5 Èõ Öù ÖõÞù ìÖåÖ¿Üë_À åùÔí ÖõÞð_ ±×ýCëËÞ Àßù. (È) ÀçùËíÞí ìärçÞíÝÖë ±Þõ Ý×ë×ýÖë Þyí ÀßäëÞí ÚOÚõ Õ©ìÖÞë ÞëÜ ÉHëëäù Ö×ë ìärçÞíÝÖëÞí ç_ÀSÕÞë VÕWË Àßù. (É) µIÀSÕÞë ±õËáõ åð_ ? ÖõÞë Àëß ÉHëëäù. ç_åùÔÞÜë_ ÖõÞð_ Üèkä ÉHëëäù. ENGLISH
VERSION
Instructions : (1)
Read the questions carefully and answer precisely.
(2)
Answer to each section should be in a separate answer book.
(3)
You can use simple calculator.
SECTION – I 1
Answer (a) and (b) both. Each answer should be in about 750 words : (a)
Ranks given by 3 judges to 10 competitors for song are as under. Compute γ for each pair by Rank differential method. Decide which pair’s ranking is nearest :
Judge − I Judge − II
1 7 5 10 3 2 4 3 5 8 4 7 10 2
Judge − III 6 4 8
9
1
2
9 1
15
6 8 6 9
3 10 5 7
OR N–1000]
4
[Contd...
(a)
(b)
(b)
Explain the concept of analysis of variance. What are the assumptions underlying in its application ? Below are given scores of ten students from three groups. Find out F value and interpret it :
9
12 14 10
8
6
7
9
8
11
Group A 13 11 12 12 9 11 8 10 11 7 Group B 15 9 20 16 11 12 14 17 10 13 Group C Compute contingency coefficient for the following data. Test the significance of it by using χ2 test and interpret it :
35 65 30
20 55 40
10 50 45
5 15
Social Levels III IV II
A B 15
I
C OR
Clarify the concept of product moment method for computing r. Compute coefficient of correlation r between scores of Maths and Science as under and interpret it :
Maths 66 72 55 82 69 75 89 59 46 62 Science 53 68 49 73 56 65 74 71 58 56
(a)
What is skewness ? If Mdn = 69.03, P90 = 78. 72 and P10 = 43. 69 for a frequency distribution, compute skewness and decide its type of skewness.
15
15
15
Answer any five of the following. Each answer should be 20 in about 125 words :
(b)
If r = 0. 73, compute the coefficient of alienation and coefficient of forecasting efficiency.
[Contd...
(c)
5
State any five characteristics of a normal probability curve.
N–1000]
2
Achievement Level
(d)
If x1, x2 and x3 are three variables and r12 = 0. 26 , r23 = 0. 28 and r31 = 0.54 . Find out the value of r12.3 .
(e)
Explain the terms mentioned below : (1)
Funducial limits
(2)
Levels of significance
(3)
Shepard’s correlation
(4)
Null hypothesis.
(f)
Enlist the uses of factor analysis. Explain nya one.
(g)
Explain one tailed and two tailed for testing a hypothesis.
SECTION – II 3
Answer any two of the following. Each answer should be in about 400 words : (a)
20
Calculate Tetrachoric coefficient for the given data and find out confidence interval at 05 and 01 level of significance : Variable x
Variable Well adjusted y (c)
Maladjusted
Successful
Unsuccessful
35
45
30
15
State the advantages of converting raw scores into σ and z scores. Convert the following scores in σ socres and z scores : 53, 41, 45, 64, 59
(c)
Derive regression equations in score form for the following data. Predict the probable score of Gaurav in Science if he has scored 45 in Math.
Maths Science Y X Mean S.D. N–1000]
50 14
rxy = 0. 70
70 17 6
[Contd...
4
Answer any five. Each answer should be in 150 words : 30 (a)
Compute S.D. of the following scores : 35, 51, 47, 32, 55, 43, 41, 62, 39
(b)
What is item Analysis ? State its importance.
(c)
Write formulas used to calculate Quartile deviation and clarify notations in each formula.
(d)
For a test of 40 items reliability coefficient is 0.55. What will be the reliability coefficient of the test, if (i)
the number of items is increased to 80.
(ii)
the number of items is increased to 120.
(e)
In the class of 80 students Sunil’s rank is 5 in Math. Calculte the PR of Sunil and interpret it.
(f)
Give names of two-two methods for estimating reliability and validity. Clarify the concept of reliability.
(g)
What is hypothesis ? State its types. State its importance in research.
N–1000]
7
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