SSB Odisha Lecturer 2018: Lecturer recruitment for non-government aided colleges, Statistics
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DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO
TEST BOOKLET Sl. No 00213
Subject Gode : 26 Subject : Statistics
LECTURERS FOR NON.GOVT. AIDED COLLEGES OF ODISHA
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RS - 19/30 (Turn over)
zo t8
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1 Joint probability of lndependent 5. A box contains 20 electric bulbs, out
events J and K is equalto : of which 4 are defective. Two bulbs
(A) P(J) * P(K) are chosen at random from this box.
(B) P(J) + P(K) The probability, that at least one of
(C) P(.t; * P(K) + P(J - K) these is defective, is .
(D) P(J) * P(K)- P(J * K) (A) 7t|e
(B) 6/1e
2. What is the marginal probability of
(c) 5t1e
dependent events and independent
events ?
(D) 4t1s
(A) One 6. A box contains 5 green, 4 yellow and
(B) Different 3 white balls. 3 balls are drawn at
random. What is the probability that
(C) Same
they are not of same colour ?
(D) Allof these
(A) 52t55
3. When we throw 2 dice then what is (B) 3/55
the probability of getting a sum 9 ?
(c) 41t44
(A) 2ts (D) 3144 ,.:,: : :
(B) 1ts
7. At a high school with 200 students,
(c) 1t12
32 play soccer, 1B play basket ball
(D) 1t3 and 8 play both sports. lf a student is
4 Two dice are thrown simultaneously selected at random, find the
what is the probability of getting 2 probability that a student plays
numbers whose product is even ? soccer or basket ball :
(A) 3t4 (A) 71t100
(B) 1t4
(c) 7t4 (c) 4t25
(D) 1t2 (D) 1t5
RS - 19/30 (2) Contd
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The probabilitythat a familyvisits city (B) 3
museum is 0.36. and the probability (C) Can not be determined
that a family rides on the 3 rivers ferry (D) 2
is 0.47. The probability that a family
11. The Centrallimittheorem tells usthat
does both is 0.22. Find the
probability that the family visits the
as sample size increases the
' sampling distribution of th6 mean
museum or rides the ferry.
(A) 0 83 . becomes:
(A) Less normally distributed but
(B) 0.61
more leptokurtic
(c) o.5a .
(B) More normallydistributed with
(D) o.6e
a larger range of scores
9. Allvalues in sample distribution that (C) More shaped like the
can freelyvaries in selected random population d istribution
sample from population are
(D) More normallydistributed with
indicated as :
a smaller range of scores
(A) Degrees of freedom
12. At a computer manufacturing
(B) Degrees of error
company, the ac'tualsize of computer
(C) Degrees of statistic
chips is normally distributed with a
(Dl Degrees of possibility mean of 1 centimeter and a s.d. of
10. You draw successive random 0.1 centimeter.Arandom sample of
samples of nine participants from a 12 computer chips is taken. Above
population, calculate the mean of what value do 2.5o/o of the sample
each sample, and plot the sample means fall?
means. lf the population has a mean (A) 1.e6
of 12 and a s.d of 6, the s. d of your (B) 1.0163
distribution is:
(c) 1 1e6o
(A) 4
(D) 1.0566
RS - 19/30 (3) (Tum over)
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13. The average sSore ofgll Pro-golfers 16. lf Va(x) 5 = and V(y) ='10, then
for a particular course has a mean of v(2x+ y) is:
70 and a s. d. of 3. Suppose 36 (A) 15
golfers played the course today. Find (B) 20
the probability that the average s@re (c) 10
of the 36 golfers exceedTl ? (D) 30
(A) q 00 17. Thedistribution function F(x) is equal
(B) 0.36e4 to:
I !--
(c) 0.0228 (A) P(X = x)
(D) lnformation lnsufficient (B) F(X < x)
(C) P(X > x)
14. A Basket ball player makes 80% of
(D) Allof these
his free throws during the season.
What is the.probability that he will 18. What would be the probability of an
make exactly 6 of his next 8 free event 'G'. lf H denotes its
complement, according to the
throws ?
axioms of probability ?
(A) 0.1468
(A) P(G1= 1/P(H) \ (: ib;
(B) 0.3355
(B) P(G)=1-P(H)
(c) 0.1678 (C) P(G)=1+P(H)
(D) 0.2e36 (D) P(G) = p1s1
15. Given x = 2 and f(x) = 0.5. lf y = 19. lf A and. B are 2 events then the
2x-3,then f(y) is equalto : probability of exactly one of them
occurs is given by:
(A) .
(A) P(A n s) + P(A n B)
(B) 0.5
(c) -2 . lq),., P(ru" f F.-ffiI-f,.?,Bffl)rR(B)
(c) P(A) + P(B) - 2P(A) P(B)
(D) 0
(D) P(A) + P(B) - P(A n B)
RS - 19/30 (4) Contd.
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20. Asurvey determines that in a locality, (B) 3 t7
33o/o go to work by bike, 42o/o goby
(c) 20 t41
car, and 12o/o use both. The
probability that a random person (D) 21 t41
selected uses neitherof them is:
o 23. At a certain university, 4o/o of men are
(A) o.zs over 6 feet tall and '1 % of women are
(B) 0.37
over 6 feet tall. The total student
(c) 0.61 population is divided in the ratio 3 :2
(D) 0.75
in favour of women. lf a student is
21. Husband and wife applyfor2vacant selected at random from among all
spob in a Company. lf the probability
those over 6 feet tall, what is the
of wifegetting selected and husband
probability that the student is a
getting selected are 317 and 213
women ?
respectively. What is the probability
that neither of them will be (A) 2t5
selected ? (B) 3t5
(A) 2 t7 (c) 3t11
(B) 5 t7 :,
(D) 1t100
(c) 4 t21
(D) 17 t21 24. What does the law of large numbers
mean ?
22. An Urn 8., contains 2 white and 3
black chips and another Urn B, (A) The more you try the more likely
contains 3 white and 4 black you are to get what you want
chips.One Um isselected atrandom (B) No matter how many times you
and a chip is drawn from it, if the chip
try, the probability remains the
drawn is found black, find the
same
'prciOability"{hat the tJrn chdsen was
Br' (C) Trying harder is a good idea
(A) 4 t7 (D) Running fora long time
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25. lf you are spinning a colour wheel (C) lnfinite
with seven colours on itand you have (D) Consistent
100 spins to get a red. After 99 spins
28. The conditionaldistribution of y given
you have gotten every color but red.
X=x,p(y=yD(=x) is:
What is the chance you will spin a red
P(Y = Y)
on the l OOth spin ? (A)
P(X = x)
(A) 1
L
(B) 1 / 100 (B) IPIX = Xi,Y = Y)
i=1
(c) 6 t7
P(X = x,'Y = y)
(D) 1 t7 (c) P(Y = y)
26. lf you are stranded on a desert and
(D)
P(X=x,Y=y)
you can't get off until you roll a six on
e(x = x)
a die, how many rolls will you ask
for? 29. The conditional expectation of Y
(A) 6 given X, E(YD( = X) is oalculated as
(B) 1
follotus:
(c) 23 k
(A) Iv, e1x = x,/ Y = y)
(D) lnfinite i=1
27 . What would be the joint probability of (B) E{E(YD())
statistically independent events that k
(C) I, v, P(v = y1l X = x)
occursimultaneously ?
(A) Zero {
(D) )Etv/X=x)P(X=x,)
(B) Not equalto zero i=1
RS - 19/30 (6) Contd
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30. Two random variables X and Y are .xx
(c) F(x,y) = J Jtt',, )dxdy
independently distributed if all of the
following conditions hold with the xy
exception of : (D) F(x, y) = I J f(x, y)dxdy
...€.g
(A) P(Y = Y lX= x) = P(! = !;
33. The (1, 1)th central moment for the
(B) E(Y)= EtE (Y/x)l
ioint P. d. f. f(x, Y) = 3 - x -Y for 0
(C) Knowingthevalueofoneofthe <x,y <1 is: I
variables provides no
(A) pr, t= - 114
information about the other
(B) tI1,1= 1112
(D) lf the conditionaidistribution of
(C) Fr,r=o
Y/X equals to the marginal
distribution of Y 1
(D)
''t,)lL^,=7-
24
31. If the Joint p. d. f. of two random
variables X and Y is defined as :
34. A man rolls a fair die again and again
until he obtains a 5 or 6. Calculate
x+y for0<x y<1 the probdbility that he will require 5
f(x, y) = 0; othenryise throws:
then the marginaldistribution of X is (A) 16t243
,. ,... ($);i'Ux) =,x + ll+ (B) 15t243
(B) fxfi) = (x + y+ 1) ' (c) 16t242
(C) fx(x) = xl112 (D) 15t240
(D) fx(x)=** 3 35. A marker is to continue shooting at
16
the target until he hits the target 6
32. The relations of cumulative
times. The probability that he hits the
distribution function with J. p. d. f,
targgt on any shooting is 0.4. What
f(x, y) of 2 dimensional random
is the probability that thE marker will
variables X and Y is : have to shoot 9 times ?
(A) F(x, y) =
ii f(x, y )dxdy
(A) 0.05e3
(B) 0.0495
(c) 0.0415
(B) F(x, y) = iit,*,Y)dxdY
" 00 (D) 0 0413
RS - 19/30 (7) (Turn over)
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36. lf a Poisson variate X is such that (A) 0.e333
P(x = 1) = P(x = 2), what is P(x = 4) (B) 0.e342
{given
"-':0.1353}: (c) 0.e313
(A) o 08 (D) 0 e383
(B) 0.082
39. Cauchy Schwartz inequality states
(c) 0.085 that if X and Y are two random
(D) o.oe variables taking real values then :
37. The chances of a Bomber hitting the (A) Et(xu2] s E(x2) Ery2)
target and miSsing the target are (B) Et(xu2l< E(x) E(Y)
3 : 2. Calculatethe probabititythatthe (c) EI(xY)3ls E(x2) E(Y2)
target will be hit at least once in five (D) EI(XY)21> E(x) . E(Y)
sorties:
40. A machine produces 10% defective
3093
(A) items. Ten items are selected at
3125
309s random. Find the probability of
(B)
3125 not more than two items being
3998
(c) defective:
3125
(D)
3093
3175
(A) (+)(*l
38. lt has been found that as an average 24( s \s
_t_t
(B)
g [roJ
the number of mistakes per typed _ .o
(c)
24 r9)"
page of a typist is 1.5. Find the I Im] 'i .rfi
probability that there are 3 or less 10
24( 9
_t
(D)
mistakes (given e-1'5 = 0.2231) : sI 1 0
RS-19/30 (8) Contd
Text of page 9
41. lf an Intemationalfilm festival, a panel 1
of 11 judges was formed to judge the
(c) c ffi; Mean 4
best film. At last two films Fo and F,
Variance = 4
were considered to be the best
where the opinion of Judges got 1
(D) c ,6; Mean = 2.5;
divided. Six judges were in favourof
Fo where as five in favour of FB. A Variance = 2
random sample of 5 judges was
drawn from the panel. Find the
43. lf x has a Rectangular distribution
probability that out of 5 judges, there f(x) = !o;-Zsx<2,then p. d.f.g(y)
were in favourof flim Fo: ofavariableY=sinxis:
100
(A)
ffi
a1
230 (A)
100
(B)
235
1
100 (B) 4vfr
(c)
231
100 1
(D) (c)
229 4(1- y)
42. lf f(x) = C * exP{- 1x2 - 6x + 9)/32; 1
- oo ( x ( -r-represents a normal (D)
a(-v)2
distribution, what is value of 'C', mean
and variance of distribution ? 44. lf x - Exponential ()"), variance y =
1
e-r'has what distribution ?
(A) C=M; Mean=3;
(A) U(0, 1)
Variance = 4
(B) N(0, 1)
(B) C=ffi;
1
Mean=3.5; (C) Gamma distribution
Variance = 2 (D) Beta distribution
RS - 19/30 (s) (Tum over)
Text of page 10
45. lf a variable X has the p. d. f. f(x) = (B) Hyper-geometricdistribution
[x expl- xl2) for 0 < x < "o, then the (C) BinomiaIdistribution
distribution has mean and variance (D) Negative Binomialdistribution
as:
49. The m. g. f. of a random variable X is,
Mean
= 2; Variance
= 4 21 4
,(A) Mx(t) = exP(2t)*
(B) Mean = 112; Variance = 114 5*5 tSexP(3t).
The expected value of X is :
(C) Mean= 4; Variance = 8
(A) 22t15
(D) Mean = 4; Variance = 2
(B) e/5
46. lf the m. g. f. of a random variable X (c) 17t15
is tt * 3 exp(t))thefi X is a :
(D) 11t5
, (A) Negative BinomialVariate 50. lf a continuous r. v. X has p. d f.
(B) BinomialVariate 1.
t (r)
(C) BernoulliVariate 5' -1Sx<0
? 0<x<1
(D) Poisson Variate 3'
' r:ii'ir
then E(X2) is equalt<j :
4t7. LetX be a r.v. U(0, 1) thenthevariate
(A) 1t9
Y= -2log X follows : (B) 213
(A) Chi-squaredistribution (c) 5112
(B) Lognormaldistribution (D) 1t3
(C) Gamma distribution 51. APoisson r. v. has Vq=2thevalue of
its mean is
(D) Exponentialdistribution
(A) 1t3
48. lf a distribution has m. g. f. Mx (t) = (B) 1t4
(2 -
"5-3,
then the distribution is :
(c) 2t3
(A) Geometricdistribution (D) 3t4
(10) Contd
RS - 19/30
Text of page 11
52. The skewness of a Binomial 56. The commulative distribution function
distribution will be zero if : of a gamma variate is known as :
(A) p < 1t2 (A) Gammafunction
(B) -p> 1t2 (B) Complete Gamma function
(C) p = 112 (C) lnconsistent Gamma function
(D) p<q (D) lncomplete Gamma function
53. The characteristic function of a 57. Let X be a random variable having
distribution is given as exp(ipt) probabUity density funtion f(x) =
11 . then
f
1+ -= by identicality, the -*
Tt 1+ x'
)(
(A) E lX lisfinite and Median does
distribution forwhich it stands is
not exist
(A) Double exponential
(B) E I X I is finite and Median is
(B) Poissondistribution
takenatx=0
(C) Cauchydistribution
(D) Exponentialdistribution (C) E I X I is not finite and Median
is taken at x = 0
54. Let X, and X, be 2 independent
random variables having the same
(D) E I X I is not finite and Median
geometric distribution. Then the does not exist
conditional distribution of X., Xt * Xz
58. Let X, X2....Xn be independent
is:
variables having exponential
(A) Geometricdistribution
distribution with parameters 0r,0, ...
(B) Poissondistribution On respectively, then z = Min(X.,, X,
(C) Cauchydistribution Xn) has exponential distribution
(D) Uniformdistribution with parameter:
55. Ahypergeometricdistribution has :
(A) ?',
(A) Two parameters
(B) Three parameters
(B) )o'lnI
(C) One parameter (c) Min(0,,,0, on)
(D) (n - k) parameters (D) Io2ln
i
RS - 19/30 ( 11 ) (Tum over)
Text of page 12
59. A relationship similarto that between 62. lf a variate X -$,(m, n), where m,
Binomial and Geometric n > 1 , the mode lies at the point :
distributions exists between : (m-1)
(A)
(m+n-2)
(A) Poisson.andExponential (m-1)
(B)
(m+n-l)
(B) Poisson and Gamma
m
(c)
(C) Poisson and Geometric m+n-2
m
(D) Poisson and Beta (D)
rn+rL
60 lf X has a geometric distribution then 63. Pearson's coefficient of skewness
for any two positive integers m and for the negative Binomial distribution
n,p(X>m+n/X>n)=; (-ilr'nq;x is:
(A) P(X > m) (p + q)2
(A)
rpq
(B) P(X < m) p
(B)
rq
(c) P(X > n)
(P+Q)2
(D) P(X < n)
(c)
PQ
(P+Q)2
6't. Which one of thefollowing probability (D)
rPQ
distributions precisely computes the
{herep= *,0= f,t
probability that there are 'x' failures
preceeding the rth success in (x + r) 6rt. If a variate X - y (cr, 1), the p. d. f. of X
trials ? is same as that of :
(A) Binomial (A) Chi-sQuaredistribution
(B) Poisson (B) Exponentialdistribution
(C) Negative Binomial (C) Normaldistribrrtiqn- r::,..,.;. .
(D) Hypergeometric (D) Weibulldistribution
RS - 19/30 (12l Contd.
Text of page 13
65. A no.rmal random variable has (B) Nominalscale
mean = 2 andvariance = 4. lts fourth (C) Ordinalscale
Central Moment Fa will be :
(D) lntervalscale
(A) , 16
(B) 64 .
69. Discrete variables and continuous
variables are2 types of
(c) 80 :
(D) 48 (A) Open end classification
(B) fime series classification
66. lf a discrete random variable takes
''3ag-."16,.;a .,. -
on"four values - 1, 0, 3, 4 with (C) Qualitativeclassification
probabilities 1/6, K, 1l4and 1 - 6 K, (D) Quantitativeclassification
where K is a constant, then the value
70. ln stem and leaf display diagrams
of Kis:' n
used in exploratory analysis, stems
(A) 1t3
are considered as :
(B) 2te
(A) Centraldigits
(c) 1t12
(B) Trailing digits
(D) 5t24
(C) Leading digits
67. Which one of the following scales is
the best scale of measurement ?
(D) Dispersed digits
(A) Nominalscale 71. Classification method in which upper
(B) Ordinalscale limit of intervals is same as of lower
(c) lntervalscale limit class interval is called :
(D) Ratio scale (A) Exclusive method
68. Which scale uses the concept of (B) Inclusive method
absolutd z5tci'? ' " ''- ""' (C) Mid-point method
(A) Ratio scale (D) Ratio method
RS - 19/30 (13) (Turn over)
Text of page 14
72. A die is thrown 1000 times and the 74. What is difference between a Bar
outcomes were recorded as follows : Chart and a Histogram ?
Out come Frequency (A) Barcharts represent numbers,
1 180
whereas histog rams represent
2 150
percentages
3 160
(B) A histogram does notshowthe
4 170
entire range of scores in a
5 150 ' distribution
6 190
(C) There are no gaps between the
lf the die is thrown once more, then
bars on a histogram
the probabilitythat it show 5 is :
(D) Bar charts are circular,
(A) e/50
whereas histograms are
(B) 320 '.
square
(c) 4t25
(D) 7t25 75. Whatisthefunction ofa contingency
' table, in the content of bivariate
73. What is the difference between
interval/ratio and ordinal variables ? Analysis ?
(A) The distance between (A) lt shows the results you would
. categories is equal across the expect to find by chance
range of interval/ratio data (B) lt sumrnarises the frequencies
(B) Ordinal data can be rannk of 2 variables so that they can
' ordered, but interval/ratio data
be computed
cannot
(C) lt list the different levels of p
(C) lnternal/Ratiovariablescontain
value for tests of significance
only 2 categories
(D) Ordinalvariables have.a fixed (D) lt compares the results you
zero point, whereas intervals might get from various
ratio variables do not statistical tests
RS - 19/30 (14) Contd
Text of page 15
76. What is the name of the test that is 79. The Coefficient of skewness is
used to assess the relationshiP always zerofor a'.
between two ordinalvariables ? (A) Symmetrical distribution
(A) Spearman's rho (B) Skeweddistribution
(B) Cramer's v
(C) Negativelyskewed distribution
(C) Chi-square
(D) Positivelyskewed distribution
(D) t-statistic
80. The degree of peakedness is
77. What is meant by a "spurious"
called:
, ,, , relationship between two variables ?
(A) One that is so ridiculously (A) Dispersion
illogical it cannot possibly be (B) Skewness
true (C) Symmetry
(B) An apparent relationship that is (D) Kurtosis
so curigus it demands further
attentiori
81 . Quartile coefficient of skewness lies
between:
(C) A relationship that appears to
be true because each variable
(A) -1and0
is related to a third one (B) 0 and 1
(D) One that produces a perfect (C) -1and+'1
negative correlation on a (D) 0 and ""
scatterdiagram
82 For Mesokurtic curve of the
78. lf mean is 25 and s.d. is 5 then
distribution, P, is :
coefficient of variation is :
(A) <3
(A) 100o/o
(B) 25o/o
(B) Zero
(C) 20o/o (c) 3
(D) s0% (D) >3
RS - 19t30 . (15) ( Turn over )
Text of page 16
83. ln uni model distribution, if mode is (B) Homoscedasticity
less than mean : (C) Multicollinearity
(A) Negatively skewed (D) lndependence of Errors
(B) Positively skewed
87. What is bo in Regression analysis ?
(C) Normal
(A) Thevalueoftheoutcombwhen
(D) Symmetrical allof the predictors are zero
84. ln Mesokurtic distribution': (B) The relationship between a
(A) Fq'3a2 predictor and the outcome
(B) Va*3o2 variable
(c) vq'3o2 (C) The value of the predictor
variable when the outcome is
(D) Fa ='3o2
ZefO I
85. Let the coefficient of determination (D) The gradient of the regression
computed to be 0.39 in a problem line
involving one independent variable
and one dependent variable. This
88. Homogeneityof 3 ormore population
conelation coefficients can be tested
result means that :
by:
(A) The relationship between two
(A) t-test
variables is negative
(B) ztest
(B) The correlation coefficient is
0.39 also
(C) 2g2 test
(C) 39% of the total variation'is (D) F-test
explained by the lndependent 89. lf there are Kgroups and each group
variable consists on'n' observation, the limits
(D) 39% ot the total variation is of intra - class correlation are :
explained by the dependent (A) 0to 1
variable 1
(B) ;to1
86. For which Regression assumption
does the Durbin Watson-Statistic 1l
(c) -;to1
Test ?
(A) Linearity (D) -1to1 '
RS - 19/30 (16) Contd.
Text of page 17
90. The formula for multiple correlation
coefficient Rz.tg in terms of
(c)'{2g.t=ffi
simple correlation coefficients
(D) Allof these
is :
'{12'll6and lra
92. lf the two lines of Regression are x +
\?z+ YZs -2^(P\zs^tts 2y - 5= 0 and 2x+ 3y -8 = 0 means
(A)
(1- v?s) ofxandyare:
(A) x-=-3,i=4
(B)
ffi
{ ("F (B) f =2,f =q'
(c) x f=2
1
(c)
m
\T
(D) f=0,f=5
93. lf the two lines of Regressions are
-1
X=
ie Y+ l; Y=-2X+ m, thevalues
(D)
M
{6 oflandmare:
(A) (= }lg;m = - 5
91. lf X1, X2 and X, are 3 variables, the (B) (.= 819; m.= - 3
partial corretation between X, and
(C) (,=-1019;m=-4
X3 eliminating the effect X1
(D) t=-819;T=0
in terms of simple correlation
coefficients is given by !h" 94. The partial correlation coefficient
formula: '{e.uis called :
v (A) Zeroorderpartialconelation
(A) Yzs.,t=
(-v?il(-v?s) (B) First order partial correlation
(C) Second order partial
(B)'{2s.t=ffi conelation
(D) Third orderpartial conelation
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Text of page 18
95. Which of the following relation is (D) Always equal to the product of-
correct ? \12,\fi,Yzz
(A) '{e.zq= \rc.2q 98. lf the sum of squares of the
(B) \,lz.z= ''lzl.g differences between the Ranks of
(c) "(rc= \zg two series is 33, then the rank
(D)
correlation coefficient is :
\tz.s= \tz.z
(A) 0.e67
96. Let the equation of the regression
(B) 0.725
lines be expressed as 2X - 3Y = 0
(c) 0.80
and 4Y- 5X = 8, Then the correlation
(D) 0 67
between X and Y is :
ftsZ 99. lf for 2 attributes A and B, AB >
(A)
/A
"l e#A the attributes are .
(B) tBT
"l/tS (A) lndependent
(c) ,w-, (B) Positivleyassociated
(D) n7 (C) Negativelyassociated
"l/tS
97. The multiple correlation coefficient (DI AttributeA>Attribute B
R,,.rg as compared to any simple 100. Range or"set of values which have
correJation coefficients between the
chances to. contain value of
variables X, X, and X, is :
popu lation parameter with pa rtic,u lar
(A) Lessthan aoy \p,\ts,\zs confidence levelis considered as :
(B) Not'less than any "1t2, \tz (A) Secondary lnterval Estimation
and y^
(B) ConfidencelntervalEstimate'
(C) Always equal to the sum of
(C) Population lnterval Estimate
\,6,'T,;,'.Y21
(D)'Sample lnterval Estimate
RS - 19/30 ( 18 ), Contd.
Text of page 19
101. For a parameter whose value is (B) Mathematically less complex
unknown, belief or claim for that (C) Computationallylucid
parameter is classified as :
. (D) Computationallyintense
(A) Parameterclaiming testing a
105. Which of the following is a wrong
(B) Expected belief testing
statement about the maximum
(C) Hypothesis testing
likelihood approach ?
(D) Primary limit testing
(A) This method doesnot involve
102. To develop lnterval estimate of any probability calcu lation
parameter of population, value which
(B) ltfindsatreethatbestaccounts
is added or substracted from point
for the valuation in a set of
estimate is classified as :
sequences
(A) Margin of efficiency
(C) The method is similarly to the
(B) Margin of error maximum parsimony method
(C) Margin of consistency (D) The analysis is perfomed on
(D) Margin of biasedness each column of a multiple
103. Considering sample size, sampling sequence alignment
distribution standard error 106. Mean squared errorof an estimator
decreases when the :
Tn of t(0) is Mlnimum only if :
(A) Size of sample decreases (A) Bias and Vo GJ both are zero
(B) Margin of error increases (B) Bias is zero and Vu (Tn) is
(C) Margin of errordecreases minimum
(D) Size of sample increases (C) Bias is minimum and Vufin) is
104. The main disadvantage of maximum
' zero
likelihood methods is that they are : (D) Bias'is not zero V, (T) is
(A) Mathematically less folded maximum
RS - 1el30 ( 19 ) ( Turn over )
Text of page 20
^and 1] arc2u. b. e of t(0)based
107. lf T nn the maximum likelihood estimator
on the random sample X.,, X, .... Xn, for0is:
then T_n is said to be UMVUE if and
only if :
(A) EX;
(A) v(rn) > v(q) (B) lxl rn
(B) v(rn) <v(q) (c) DJK/.
(c) v(rn)= v(q) (D) \x2 t Ji
(D) V(Tn = V(4) = t
111. A family receives 1, 2 and 3 wrong
108. The denominator in the Cramer Rao
telephone calls on 3 randomly
lnequality is known as :
selected days. Assuming that the
(A) lnformation limit wrong calls follow Poisson
(B) Lower bound of the variance distribution, the estimate of the
(C) Upper bound of the variance number of wrong calls in 6 days is :
(D) Both lower and upper bounds (A) 6
with infinite
(B) 12
109. Efficiency of sample mean as (c) 36
compared to median as an estimate (D) 48
of the mean of a normal population
112. A random sample of 16 houses has
an average body weight 52 kgs and
(A) 64 percent
s.d. of 3.6 kg. 99o/o central
(B) 157 percent
confidence limits for body weight in
(C) 3'17 percent
general are {Given trso.or = 2.95} :
(D) 315 percent
(A) (5a.66; 4e.345)
110. lf X, Xr.... Xn is a random sample (B) (52.66; 51.34)
from the population havingthe density
(c) (52.28;48.72)
1 -tr x2/
function f(x, 0) =
m" " " lhen (D) (50.28; 43.72)
RS - 19/30 (20) Contd
Text of page 21
113 Least square estimators "under 117'. Foran estimatorto be consistent, the
linear set up are :
unbiasedness of the estimate is :
(A) Unbiased
(A) Necessary
(B) UMVUE',S
(C) BLUE's (B) Sufficient
(D) Allof these (C) Necessary as well as sufficient
114 The M. L. estimators are necessarily: (D) Neither necessary nor sufficient
(A) Unbiased 118. Formula for Statistic-Chi-square for
(B) €ufficient
the Binomialfrequencies a and b to
(C) Most efficient
occur in a specified ratio r: 1 is :
(D) Unique
r(a - b)2
115 A confidence internal of confidence (A)
r(a + b)
coefficient (1 - q) is the best which
(a - rb)2
has: (B)
r(a + b)
(A) Smallest width
(a - rb)2
(B) Vastest width (c)
r(a + b)2
(C) Upper and lower limits
equidistant frorp the parameter (ar - b)2
(D)
r(a + b)
(D) One side confidence interval
119. A normal population has a mean of
116 For a Random sample from a
Poisson population P(tr), the 0.5 and s, d. = 6. The probabilitythat
maximum likelihood estimate of l" the sample mean of 625 items of a
IS: sample will be negative is :
(A) Median (A) 0.0188
(B) Mode (B) 0.365
(C) Geometric mean (c) 0.4812
(D) Mean (D) 0.135
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Text of page 22
120. Given the following sample of (B) 16
8 observations, - 4, - 3, - 3, O, 3, 3,
(c) 41
4, 4 lhe value of students t-test
(D) 38
Ho,tr=0is'.
(A) 2..73 123. The can be defined as
(B) 0.e7 the sequence of identical occurrence
(c) 3.3 of the elements (numbers of
symbols). preceded or followed by
(D) 0.41
different occurrence of the elements
121. For testing Ho : o = oo in a normal
or by no elements at all :
population N(0, d), a CriticalRegion
based on sample X,,Xr.... Xn is
(A) Mann-Whitney'U'test
(B) KruskalWallistest
I, xi < K. For which alternative
hypothesis does this provide (C) Friedman Test
uniformly most powerfultest : (D) Runs test
(A) o*oo 124. You have conducted a study
(B) o'= ot '
comparing Army, Navy arld RAF
(C) 6. Go cadets ast measure of leadership
(D) o, oo skills. There are unequalgroup sizes
and the data is.skewed so you need
122. The claimed average life of electric
to use a NP-test. Which test you
bulbs is 2000hrs with a s.d. equals
choose ?
to 250 hrs. To make 95% sure that
the bulbs should not fall below the (A) Wilcoxon
claimed average life by more than (B) Friedman
5%,the sample size should be : (C) MannWhitney
(A) 24 (D) KruskalWallis
RS - 19/30 (22) Contd.
Text of page 23
125. The null hypothesis of the sign test is 1?l. What would be the ideal test for a
that: single large enough sample with
,a
categorical data!
(A) Haf tne ranks to be less than
. median and'half greater than
(A) Chi-square test
median
(B) Fishers exacttest
Half the ranks to be less than
(c) ANOVA
Pl (D) One samplet-test
mean and half greaterthan the
mean 128. lit the sample size in Wald-Wolfwitz
(C) The lowerhalfthe ranksto have runs test is large, the variate R is
distributed with mean :
the same mean as the upper
lrr (A) _+1
2m
m+n
(D) -Thelorrverhalf the ranksto have
2n *1
the same s. d. of the upper half (B)
m+n
126. The null hypothesis for the Mann- 2mn
(c)
m+n
. Whitney U-test is used to test that :.
2mn
,,, (A)., Iwosamples arefromdifferent (D)
m+n
populations -+1
129. While performing Kruskal-Wallis test
(B) Twosamples arefromdifierent
the Ranks are assigned :
populations but have the same
mean
(A) lndependendently to the
observation for each treatment
(C) Two samples are from the
same poputations and havethe
. (B) For observations in each block
same mean '
' independently
(D) Two samples are from the (C) By pooling allthe observations
. same population and have the (D) lndependently taking the
same median observations deviations
RS - 19t30 (23 ) (Turn over)
Text of page 24
130. lf there are 3 items and number of 1 33. A sample consists of :
Judges is two, then the probabilities
$) Allunits of the population
of occurrence of the value of y. as (B) Anyfraction of the population
- 1 , - i, i, l are respectively :
(C) 50% units of the population
(A)
1111 (D) 5% units of the population
4'4'i'4
(B)
1111 134. When an lnvestigatorwants a sample
6'3'3' 6 containing 'm' units which posses a
1 1 1 1 rare attribute, the appropriate
(c)
6' 3'3 '6 sampling procedure is :
(D)
1111 (A) SRSWOR
a'6'e'e
(B) Stratified sampling
131. ln NP-statistic, usuallythe confidence (C) lnverse sampling
interval is found outfor: (D) SRSWR
(A) Population Medium 1 35. The most important factor in
(B) Population Mean determining the size of a sample is:
(A) The availability of resources.
(C) Both (A) and (B)
(B) Purpose of survey
(D) Neither(A) nor(B)
(C) Heterogeneity of population
132. Kruskal Wallis H statistic with K (D) Completeenumeration
treatments and n blocks which is 136. lf 'n' units are selected in a sample
approximated to Chi-square has d.f : from N population units, the sampling
fraction is given as :
(A) (n - 1)
(A) Nl/n
(B) (K-1)(n-1)
(B) 1/N
(c) (K - 1) (c) 1tn
(D) K(n - 1) (D) n/N
a
RS - 19/30 (24) Contd
Text of page 25
t
137. Stratified sampling comes undeithe 140. ln systematic sampling, value of K is
category of : classified as :
(A) Restrictedsampling (A) Sampling lnterval
(B) Subjectivesampling
(B) Sub-stage lnterval
(C) Purposive sampling
(C) Secondary stage lnterval
(D) Unrestrictedsampling
(D) Multi-stage lnterval
138. Whicn one problem out of the four is
not related to stratified sampling ? 141. Mistakes of biases are considered
(A) Fixing the criterion for as causes of non-sampling errors
stratification must includes:
(B) Fixing the number of strata (A) lncorrect enumeration of
(C) Fixing the sample size population
(D) Fixing the poin.ts of (B) Non-Randomsampleselec{ion
demarcation between strata
(C) lncompletequestionnaire
139. In sampling without replacementthe
(D) Allof these
standard error of sampling
distribution of sample proportion f is 142. A sample of 16 items from an inifinte
equalto : population having s. d. = 4 yielded
/N-n\ total scores as 160. The S. E. of
(A) pqIN-r.J
sampling distribution of mean is:
pq (N'- n )
(B)
;[Nr.l (A) 1
(B)
(c)
pq -n
n N-1 (c) 40
(D)
Jpq f ru-n) (D) .45
" IN-1./
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Text of page 26
143. A population of N units is divided t+s. ine ratio estimrt" f^K is the "best
,
into 'K' strata. A sample of size 'n' is linear use of V when, the relation
to be selected. Let N, the Jth between v. and x. is I
stratum size and n, the sample size
(A) v 0xr
from it (J = 1 ,2.... K). Then formula
(B) v Fxi +e.I
for selection of n, under proportional
(c) Yi= g'i * ei
allocation is:
(AI n,=
N (D) pr-Yi q
J6 -
N 146. A market researcher randomly
(B) nr.=[
selects 500 people from each of 10
cities:
nJ=n
(c) NJN (A) Simple Random
(D) nrN., = Nn (B) Systematicsampling
(C) Stratified sampling . . -_
144. Ratio estimator is better estimate of
(D) Conveniencesampling'
V than sample mean based on
SRSWOR if :
147. Replication in an experiment
A
means:
(A) MSE(YR) < Varr*r(7)
A (A) The number of Blocks
(B) MSE(YR) > Var.*s(f)
A (B) Total number of treatments
(C) MSE(YR) + va([)
(C) Total number of times a
treatment occurs in an
MSE
(D)
[*.J experiment
Var(y)
(D) Fraction to be sampled
RS - 19/30 (26) Contd.
Text of page 27
148. The formula for determining the experimental units through a random
number of replications 'r'with uaual
pressure are categorised as :
notation is:
a
(A) r = 2t2os2ld2 (A) C. R. D.
(B) t= J2tos2ld2 (B) Partially R. B. D. '
(C) r =t2o"2td2 (c) R. B. D.
(D) r=2tas/d
(D) L. S. D.
149. ln case of a random effect model, the
hypothesis which is to be tested with 152. ln the R.B. D. with 'b' block and 'v'
regarded to the treatments is : ' treatments the error degrees of
(A) ,i= o
freedom are:
(B) Zr? = o
(A) b(v- 1)
(c) Xti= o
(D) oi=o (B) (b-1)(v-1)
(c) v(b - 1)
150. If an experiment involves 2 or more
treatements are fixed and the others
(D) (b2- 1)
are of random nature, one should 153. ln a Randomised block design with
choose: 4blocksand 5treatments having one
(A) Mixed effect model missing value, the error degrees of
(B) Random effect model freedom willbe :
(C) Componentof variance model (A) 12
. (D) Anova model (B)
. 11
151. The experiments in which the (c) 10
treatements a(e allocated to (D) e
RS - 1el30 (27 ) (Turn over)
Text of page 28
154. lf a stratified sample of size 45 is to (c) 7r
be selected by Neyman allocation (D) 8r
population with N,, = 150, Nr= 350,
157. ln a design of experiment with 5
S? = 4, s'r= 9, then the number of
factors each considered at 2 levels,
units to be selected from the first
the key block is given as
stratum is:
(A) 10 BC, DE, BCDE, ABD, ACD, ABE,
ACE. Which one of the following
(B) 75
gives confounded interaction ?
(c) 35
(D) 20 (A) ABC, ACE, BCDE
(B) ADE, ABCD, BCE
1 55. Which one of the following refers to
the deliberate introduction of non-
(c) AcE, ABD, BCDE
orthogonality in a Design ? (D) ABC, ADE, DCBE
(A) Confounding 158. A factorial design in which both
(B) Randomisation dependent variables involve random
(C) ErrorControl assignment is referred to as a
(D) LocalControl, factorial design.
1 56. For a 23 factorial design with r (A) Within subjects
replications, what is the errord. f. is : (B) Mixed
(A) 6(r- 1) (C) Correlated-groups
(B) 7(r-1) (D) Between subjects
RS - 19/30 (28) Contd
Text of page 29
159. Giver!N = 120and n = 8. Which one 162. A population of size 100 is divided
among the following represents a into 3 strata with sizes 50, 30 and 20
balanced systemaiic sample :
respectively with equal variance.
(A) {3,33,63, 93, 2gi,5g,gg, 11g}
What are the stratum sample sizes
(B) {7, 17,27, 37, 47, 87,97, 107}
under proportional allocation for a
(c) {3,32,62, 92,25, 55,85, 110}
fixed samplesize20?
(D) {5, 15,25,35,45,85,95, 105}
(A) 4, 9 and 7
'
160. GiventhatN = 500, n = 50, i = 125,
) (B) 6, 9 and 15
i = 250, X = 150. Then the ratio
(C) 10, 6 and 4
estimator of Y is :
(A) 325 (D) 8,7 and 5
(B) 375 1 63. ln a23-factorial experiment, principal
(c) 300 blocks of replicates 1 and 2
(D) 400 respectively consists'consist of {( 1 ),
a
161. Which of the following principles of A, B, C,ABC}and {ABC,AC, B, (1)}
experimentation is / are used in the What are the confounded interaction
case of CRD ?
effects in the two replicates
(A) Localcontrol
respectively ?
(B) Randomisation and Local
(A) ABC and AB
control
(B) BC and AB
(C) Replication and Localcontrol
a
(D) Replication (C) AB and BC
and
Randomisation (D) BC and AC
RS - 19/30 (2e ) (Turn over )
Text of page 30
1 64. lnANOVAfor one way classified data 165. lf I is the mean of a simple random
sample of size 'n'drawn from a
with 3 classes and 3 observations per
population of size N, then what is the
class, F value is 15 and totalsum of
V(V)SRSWOR
squares is 12. What is the mean Ratio
ti-y)SRSwR equalto :
square between classes ? (N-1)
(A) (- _.)
(A) 2
(N-n)
(B) 3 (B) (N:1)
(c) 4
(D) 5
(c) #
(D) H
rrlartttttltllr
a
a
RS - 19/30 (30) Contd
Text of page 31
SPACE FOR OUGH WORK RS - 1e/30 (230) (31 ) Statistics
Text of page 32
J
IIJ
a
1Official key not published for this paper.
Page 1 of 32
Source: State Selection Board. Question paper published by State Selection Board.