SSB Odisha Lecturer 2021: 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. 015 6
Subject Code : 26 Su : Statistics
LECTURERS FOR NON.GOVT. AIDED COLLEGES OF ODISHA
TimeAllowed:2 Hours Maximum Marks : 150
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tw- 18/9 2024- (Tum over)
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1. The sum of two positive quantities is (c) 0.10
2n. Find the chance that the product (D) 0.21
of the two quantities is not less than
4. Asurvey determines that in a locality,
3/4 times their greatest product :
33% go to work by bike, 42o/o goby
(A) 0.30
car, and 12% use both. The
(B) 0.50 probability that a random person
(c) 0.25 selected uses neitherof them is:
(D) 0.45 (A) 0.3e
2. Theprobabilitythatateacherwill give (B) 0.37
an unannounced test during any (c) 0.63
class meeting is 0.2. lf a student is (D) 0.7s
absent twice, what is the probability
5. At a certain university, 4% of men are
that he will miss at least one test ?
over 6 feet tall and 1 % of women are
(A) 0.o4 over 6 feet tall. The total student
(B) 0.80 population is divided in the ratio 3 : 2
(c). 0.60 in favour of women. lf a student is
(D) 0.36 selected at random from among all
those over six feet tall, what is the
3. CompanyAproducesl0%defective probability that the student is a
products, company B produces2Oo/o
woman ?
defective products and company C
(A)
I
produces 5% defective products. lf 11
choosing a company is an equally 3
likelyevent, then find the probability
(B)
t
that the product chosen is defective : 3
(c)
11
(A) 0.22
1
(B) 0.12 (D)
^
tw- 18/9 (2) Contd.
Text of page 3
6 For some constant c, the random 8. Pick out the correct relation among
variable X has probability density different modes of convergence of a
function:
sequence of random variables :
ttx) =
[cxn. ocx<1 (A) Convergence almostsurely +
{0, othenrise convergenc.e in distribution
Find P(X > x). =+ convergence in probability
(A) xn*1 - 1
(B) Convergence in r-th mean =+
(B) *n+1
convergence almost surely =+
(c) 1
convergence in probability
(D) 1 - xn*1
(C) Convergence in probability
7 lf a random variable X has the density
+ convergence in r-th mean
function
+ convergence in distribution
*e-lxl , -6(X(oo (D) Convergence in r-th mean =+
f(x) ={
0, otherwise
convergence in probability +
the distribution function is given by: convergence in distribution
ax
r-.x <0 9. Let {Xn} be a sequence of
2',
(A) F(x) = ax
independent random variables with
1-|,x>o E(xk) = F*and V(xk) = o2*. Then,
lim
6x
r-.x< Q 1:n o3-o=
n-)oo n2"k=1-k
2',
(B) F(x) =
6-x
>o
x
I =,,** -'l =', [rk P 0
'-7'x n -)
6-x This theorem is called :
(C) F(x) = 1-i-,0<x<-
1, otherwise (A) Bernoulli's theorem on WLLN
(B) Khinchin'stheoremonWLLN
ax
'l- " .x<0
2' (C) ChebysheVstreoremonWLLN
(D) F(x)= 6-x
" .x>0 (D) Poisson's theorem on WLLN
2
rw- 18/9 (3) (Tum over)
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10. Lindeberg-Levy Central Limit
Theorem assumes that the sequence
(D) --T
e2t -1
of random variables under 12. Let X and Y be jointly distributed
consideration are: continuous random variables with
!oint probability density function
(A) i.i.d. with a common mean and
a common variance (< "") . Ju"-('x+3Y), x,y> o
f(x, y) =
(B) i.i.d. Bernoulli variables with I o, otherwise
Find E(YIX > 2) :
common parameter p
(C) independent with different (A)
1
3
means and d ifferent variances
2
(."") (B)
3
(D) independentand theirthird and
1
higher order moments exist (c)
6
11. Find the momentgenerating function 3
(D)
5
of X if its probability density function
is 13. lf a binomialvariate has mean 4and
variance 3, find its third central
x forO<x<1
f(x) = moment pa:
2-xfor1<x<2'
1
(A)
t+l
2
(A)
5
(B)
2
(B)
[+)' (c)
3
2
3
(c) Iezt - r)2 (D)
4
[t )
tw- 18/9 (4) Contd
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14. lf X - N(p, o2), find variance of (B) 36
1(x-rr)2 (c) 144
z[".] (D) 16
1 17. Which one is not a condition of a
(A)
4 Poisson model with probability of
1
having success p ?
(B)
2 (A) p in a smal! time interval is
(c) 1 constant
1
(B) p more than one in a smalltime
(D) interval is very small
8
(C) p in a small time interval is
15. lf a random variable X has a beta
independent of time and also
distribution of the first kind with
of earlier success
parameters m > 1 and n > 1, the
(D) p in a small time interval
mode lies atthe point:
(t, t + dt) is kdt for a positive
m constant k
(A)
m+n-2
18. Buses arrive at a specified stop at
m-1
(B) 15 minutes intervals starting at 7 A M.
m+n-1
lf a passenger arrives at the stop at
m-1 a time that is uniformly distributed
(c)
m+n-2 betrrueen 7 and 7 : 30, find he probabiltty
m that he waits less than 5 minutes for
(D)
m+n a bus:
16. The lifetime (X) in hours of a certain 1
(A)
electrical equipment has a normal 6
distribution with mean 80. However, 2
(B)
experience shows that life times of 3
approximately 99% of the said 1
(c)
equipment lie in the interval [68, 92]. 3
Find variance of X: 3
(D)
(A) 25 4
tw- 18/9 (5) (Turn over)
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19. Find the variance of the number of (B) Histogram
times one must throw a die unti! the (C) Frequencycurve
outcome t has occurred 4 times : (D) Frequencypolygon
(A) 144
23. curve is used to study
(B) 120 disparities of the distributions of
(c) 124 income and wealth for certain
(D) e6 segment of a population.
20. lf X and Y have a bivariate normal (A) Ogive curve
distribution with means F74 = 12, (B) Frequencycurve
[r, = 10 ; standard deviations o* = 30, (C) Range curve
o, = 20 and correlation coefficient (D) Lorenzcurve
p = 0.8, find E(XIY = 9) :
24. 120 students appea;ed fora certain
(A) 12.00
test and the following marks
(B) 10.80 distribution was obtained. lf 35
(c) 13.20 marks are required for passing, find
(D) 12.53 an approximate number of failed
students:
21. For the frequency distribution with
classes of unequal widths, the Marks Students
heights of bars of the histogram are o -20 10
proportionalto : 20 -40 30
(A) Frequencies in percentage 40-60 36
(B) CIass intervals 60-80 30
(C) Frequencydensities 80- 100 14
(D) Class frequencies (A) 33
22. The suitable graph to representthe (B) 17
time series data is : (c) 41
(A) Historigram (D) 35
tw- 18/9 (6) Contd.
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25. Karl Pearson's coefficient of
(c) Hu 1
6X
skewness of a distribution is +0.40
wfiose mean and standard deviations 5
(D) H uh
are 30 and 8 respectively. Find the
mode of the distribution : 28. The first normal equation, for fitting a
(A) 28.e cury.e of the type y = abxto a data set
(B) .26.8 (x,, y;), i = 1,2; ...., n by the least
(c) 21.8 squares method, is Ilog y = n log a +
(D) 18.5 log b Ix. The second equation is:
26. The first three moments of a (A) )xlogY= log a 211+|og b >x2
distribution about ,"ir" 1 are 2,25 (B) Ix log Y = log a Xx + log b (Xx)2
and 80 respectively. Find variance (C) >lngY= log a xx+ log b (x)2
u^:
and .J
(D) >f togy= log alxlogY+ log b
(A) 21 and - 54
IxElogy
(B) 21 and-30
(C) 16 and - 71 29. ln a very hotlyfought battle, at least
(D) 25 and - 44 70% of ttge combatants lost an eye,
at least 75% lost an year, at least
27 . Arithmetic and harmonic means of x,,
80% an arm and at least 85% a leg.
i=1,2,...., n, aref and h respectively.
Find at least what percentage of
Then the harmonic mean Hu of u, =
combatants lost all four :
1
6\ ,i= 1,2, ...., n, is given by (A) 17o/o
1
(B) 19o/o
(A) H
u 6h
(c) 15%
(B) Hr=
*,. (D) 1oo/o
rw- 18/9 (7) (Tum over)
Text of page 8
30. lf X and Y are two conelated variables (B) 0.37
having the same standard deviation (c) 0.52
o and the correlation coefficient p, (D) 0.25
then the corretation coefficient
' betweenXandX+Yis: 33. For a trivariate distribution in X.,, X,
and Xa, all the total correlation
1 coefficient between the variables are
(A)
W equal, say cL lf Rr.r. is the multiple
correlation coefficient of X,, on X,
+
o
(B) and X., then 1 - R?.r, is equalto :
,m6
(A) (1 -a)(1 +2a)/(1 +s1
(c) [.p (B) (1 + s) - (t - cr) (1 + 2ct)l / (1 + cr)
'l 2 (C) (1 - cr) (1 - 2o) / (1 + cx)
(D) @ 2o
(D) (1 + cr) (1-2a) t(1 - cr)
31. Thetwo regression equations of Yon 34. lf p and I are respectively the
conelation coeffi cient and mnelation
XandXonYareY=0X+4and
ratio while dealing with two variables
X = 4Y + 5 respectively. A plausible
intervalfor 0 is : X and Y then which one of the
following statement is nottrue ?
(A) (0,0.25)
(B) (0,0.50) (A) rlis an appropriate measure of
(c) (0. 20,1.0), curvilinear relationship
between the variables
(D) (0, 1.0)
(B) When both variables are
32. The coefficient of rank conelation of dichotomous, I is more
the marks obtained by 10 students
suitable than p to measure
in two subjects was 0.4. But, later it
association between them
was found that the ditference in
ranks for one student was wrongly
(C) 1-rt2 <1 - p2
taken as 2 instead of 3. Find the (D) The value of n is not
correct coefficient of rank independent of the
conelation: classification of data on the
(A) 0.43 variables
rw-18/e (8) Contd
Text of page 9
35. When a random samplexl, )g, ..., xn 38. The modal value of a F.distribution
is taken from a normal population with (8, vr) degres of freedom is
N(p, o2), the variance of the sample 7t12.Compute vr.
(A) 5
variance s2 = lt,t_.(*, - x)2 is:
tt t- I
(B) 7
(A) z/:tn (c) 11
(D) 10
(B) &tzn
39. lf 262n is a chi-square variate with n
(C) zoaln
(D) o4tn2 degrees of freedom, then
ff *,,,
be distributed as a :
36. lf X and Y are independ ent y2
(A) Chi-squaredistribution
variates with 6 and I degrees of
(B) Exponentialdistribution
freedom, then XAf is a :
(C) Gamma distribution
(A) p1(3,4) variate (D) Fisher'st-distribution
(B) f variate with 14 degrees of 40. lf X has a F-distribution with (m, n)
freedom degrees of freedom, then the
distriblrtion of 1 /X will be :
(C) F(5, 7) variate
(A) t-distribution with n degree of
(D) p2(3,4) variate
freedom
37. For4 <n < 30, thetdistribution curve
(B) F-distribution with (; ;)
with regard to flatness is :
degrees of freedom
(A) Mesokurtic
(C) F-distribution with (n, m)
(B) Bimodal degrees of freedom
(C) Leptokurtic (D) Chi-square distribution with m
degree of freedom
(D) Platykurtic
tw- 18/9 (e) (Tum over)
Text of page 10
41. property ensures that the (B) lt is a function of the sufficient
d ifference between the estimator Tn statistic
and the estimable parametric fu ndion (C) lt is asymptotically normally
y(0) decreases as the sample size n distributed about the true
increases indefinitely. parametervalue
(A) Sufficienry (D) lt is uniformly minimum
variance unbiased
(B) Consistency
(C) Unbiasedness 44. Which of the following is the most
commonly used estimation tool in
(D) 'Efficiency
regression analysis ?
4i. lf x- is the sample mean based on (A) Methodofmoments
random sample of size n drawn from
(B) Method of minimum chi-square
the exponential distribution f(x) =
(C) Method of leastsquares
Oe4t, 0 S x < oo, 0 ) 0, an estimator
(D) Method of maximum likelihood
of the parameter 0 obtained by the
method of moments is: 45. Let U be the set of all unbiased
estimators of y(0), V 0 e @. An
(A) 1tV
eStimator To e U is such that
(B) 1tx-2
Ve(To) < VeO) for all 0 e@ and for
(c) r every T e U. Then To is called :
(D) 72 (A) MVB estimator of y(0)
43. Which one of the following (B) UMVU estimator of y(0)
statements about a maximum (C) The most efficient estimator of
tikelihood estimator, if exists, is not Y(e)
true ? (D) Minimalsufficientestimatorof
(A) lt is consistent Y(e)
lw-'18/9 (10) Contd.
Text of page 11
46. For a Cauchy's distribution whose the maximum likelihood estimator of
probability density function is given p is:
1 (A) x
bYf(x) = ,-oo(X(ool
"[r*(*-e)2] (B) x /N
(A) The sample median is an (C) ni/N
unbiased and consistent (D) 7 tn
estimator of the population 49. Consider a random variable X with
mean probabilig density func'tion f(x). Then
(B) The sample mean is an forwhich of the following there does
unbiased and consistent not exist a sufficient statistic for 0 ?
estimator of the population
1
mean (A) f(x) =
(C) The sample mean is a biased
;[,.d,n , -o(f,(o
but consistent estimator of the x
(B) f(x) ,0(x<0
population mean 0
(D) The sample median is an
(c) (x) =-a2n-,-l(, - o)2 r-oo(X(o
1
unbiased but not consistent
estimator of the population 1
mean
(D) (x)
e
e-/o, ocx< -
47. lf a random sample x, x2,....., xn is 50. A student conducted a study and
taken from a normal population reported that the 95% confidence
interval for the population mean rias
N(0, o2), the Cramer-Rao lower
bound for estimating o2 is : [46, 52]. He was sure that the
population SDwas 16. Whatwasthe
(A) 2o2 ln
sample size (rounded tothe nearest
(B) go2 tn2 whole number) used to computethe
(c) oa t2n said interval?
(D) 2oa ln (A) 62
48. lf i'is the sample mean based on a
(B) e7
random sample of n observations
(c) 1oe
from a binomial population B(N, p), (D) 40
rw- 18/e ( 11 ) ( Tum over )
Text of page 12
51 . The p-value of a test is the : 53. !f a random sample x1,x2,...., xn is
taken from a normal population
(A) Largest significance level for
N(0, 1), then the best critical region
which the null hypothesis can be
of size aunderthe Neyman-Pearson
rejected
paradigm to test the hypothesis
(B) Smallest significance level at Ho : 0 = 0 against H,, : 0 = 1 is
which the null hypothesis can be given by:
rejected
(A) |-rosro. rt,ri.|*logko
(C) Smallest significance level at
which the null hypothesis can be (B) ,l= ,, . 1+ !os ko
,
acbepted
(c) tn
-i=1 *, . 1- los ko
(D) Probability that no errors have
been made in rejecting or (D)
accepting the null hypothesis
'l=,,*,'l+logko
54. A test based on a critical region W
52. When a coin is thrown independently
of size a for testing Ho : 0 = 0o
4 times to test the hypothesis that the
against a composite alternative
probability of heads is I versus the
H, : 0 * 0o is such that P{x e WH1} >
alternative that the probabili$ is f ,
P {x e W1/Hl } for all 0 * 0oand for
the size of the type- 1 error is :
every critical region W, of size o.
5
(A) 16
Then the test is called :
16
(B) z7 (A) A most powerfultest
11
(B) An uniformlymostpowerfultest
(c) 16
(C). An unbiased test
11
(D) n (D) A most powerful unbiased test
tw- 18/9 (12) . Contd.
Text of page 13
55. Point out the incorrect statement 58. lt is thought that 20% ol all students
regarding the likelihood ratio test: taking a particular course received
(A) Likelihood ratio is a random a grade of A. tn a sample of 100
variable lying between 0 and 1. students, it is found that 15 made an
A. What is the calculated value of the
(B) Thetestisgenerally UMP ifan
UMPtestexists. test statistic for testing the true
proportion is 2070 under large
(C) Under certain conditions, the
sampletheory?
likelihood ratio is normally
distributed.
(A) 1.40
(Ol The test'is asymptotically (B) 3.12
consistent but not necessarily (c) 2.35
unbiased. (D) 1.25
56. Median test utitizes: 59. Genetic theory states that the
(A) Hypergeometricdistribution proportion of chitdren of the parents
(B) Negativebinomialdistribution of three different blood types M, MN
and N on the averagewilt be 1 :2:1.
(C) Binomialdistribution
But a survey report states that in a
(D) Poissondistribution
random sample of 300 children, the
57 . lf the sample sizes n, and n, of the numbers of children belonging to the
two samples are large, the distribution types M, MN and N were respectively
of Mann-Whitney U statistic is 90, 135 and 75. Value of chi-square
asymptotically normal with variance : statistic for 2 degrees of freedom
calculated from the data in order to
nrnz (nr + ne )
(A) testthe conespondence between the
12
theoretical ' and observed
nrnz(nr+ry+1)
(B) frequencies is:
12
(A) 4.50
nrnz (q nz + 1)
(c)
12
(B) 4.17
qrb(q+u-t)
(c) 11.25
(D) (D) e.03
12
lw- 18/9 (13) (Tum over)
Text of page 14
60. lt is known that for right-handed (D) Non-sampling errors in a
people, the dominant (righQ hand sample survey can be
controlled to a greater extent
tends to be stronger. For left-handed
than in case of a census survey
people who live in a world designed
for right-handed people, the same 62. When a sample of 10 units isdrawn
from a population of 110 units both
may not be true. To testthis, muscle
by simple random sampling without
strength was measured on the right and with replacements, what is the
and left hands of a random sample percentage relative gain in efficiency
of 15 left-handed men and the of the former over the tater for
estimating population mean ?
difference (left+ight) was found. The
alternative hypothesis is one-sided
(A) 11.2%
(left hand stronger). The resulting
(B) 8.2o/o
t-statistic was 1.80. This is an
(c) e.0%
(D) 10.0%
example of :
(A) Atwo-samplet-test 63. Fora stratified random sampling,let
*,,
(B) A paired t-test S and C, respectivety be size,
variance and cost of the survey per
(C) A pooled t-test unit in the jth stratum. Then the
(D) Aone-samptet-test optimum sample size for jth stratum
that minimizes variance of the
61. Which of the following statements is estimate for a specified total cost is :
incorect for a sample survey ?
NjSj/ j
(A) A sample survey is a time (A) nj= n Lj NjSj /
saving and cost reducing
method
ru,s1 trE
(B) A sample survey is subject to (B) n.=n
I );ru;sJ rf,
both sampting and non-
sampling errors NjSjCj
(c) ni=nI,iN
(C) Sampling errors can be jsic j
completely eliminated from a Nisl6
sample survey (D) n.=n
I ,jNjs1 {q
tw- 18/9 (14) Contd
Text of page 15
{_
64. While talking about the merits and (c) p t 1.96 -n p(t-p)
nN
demerits of multi-stage sampling,
which one of thefollowing stiatements
(D) p+
is not true ?
(A) lt reduces the costs and time 66. A random sample of 10 units is drawn
associated with data collection from a population of 100 units by
(B) Provides flexibility by allowing simple random sampling with
replacement in orderto estimale the
different sampling methods at
differentstages
ratio = V I x, where V and I aie
population means of y and x. lf it is
, (C) The sdmpb will not be 1O0o/o known that V = 10, X= 5 and 6 =
representative of the entire
,l:: (Y,- Rx,)2 = 5oo, rind variance
, population
of the ratio estimator:
(D)t Normally more accurate than
(A) 0.18
simple random sampliqg with
(B) O.2O
the same sample size ,
(c) 0.02
65. For estimating P, the proportion of (D) 0.03
units in a population of size N
possessing an attribute, a simple
67. When the nirmber of units in the
population is not an integral multiple
random sample of n units is drawn
of sample size, the systematic
by without replacement. Then 95%
sampling procedure adopted is
confidence limits for P under normal
called:
approximation using unbiased
estimator p (sample proportion) are :
(A) Circularsystematicsampling
(B) Linear systematic sampling
N-n p(t
p r 1.96 - p)
(A)
6lN (C) Two-dimensional systematic
sampling
N-n
-p) +-
1
(B) pt 1.96 n-1)N 21 (D) . Balanced systematicsampling
tw- 18/9 a.
(15) ( Tum over )
Text of page 16
68. Suppose that a random sample of n the village as an auxilliaryvariable. lf
units is drawn from a finite population the total cultivated area under the
of N units with unequal probabilities block is not known, whatwould be the
without replacement with y, as the appropriate sampling design to be
used ?
measurement for the ith unit. Let zr,
be inclusion probability of ith unit in (A) Conventional two-stage
the sample, and ru,, be the joint
. sampling
inclusion probabilityof ith and jth units .(B) Stratified two-phase sampling
in the sample. For estimating (C) Conventional two-phase
population totalwhich of the following sampling
is not a correct expression for the (D) Two-phaseclustersampling
variance of the Horvitz-Thompson 70 lf a sample of 2 units is drawn from a
estimator ? population of N units by PPS
2 sampling without replacement with P,
(A)
1
2
t N Yi_Yi
i*j ("pi- "i1\ Tti ni as the probability of selecting ith unit
at the first draw, then the probability
(B) N2 ,,1,, ri\,{,*, -,,, )[f -#,,)' of selecting ith unit at the second
draw is :
2
(c) ,,1,rl,,(n,*i - r,)[+ -
il (A) p.p.( t * '' 'l
, ,[1_Pi 1_Pj)
(D) ,,l,,Tri *z:.Nr-1-INj> (q-*q)
aq\ YiYi
DD.
(B) P.+E. 'l'l
I l*,1_pj
69. ln a crop survey it is desired to
estimate total area under mustard in ElD.
t*r1_Pj
a block by regression method of
estimation considering village as the (D) -!-* j-
1-q 1-Pj
sampling unit and cultivated area of
rw- 18/e ( 16 ) Contd.
I
Text of page 17
71. Local control helps to : (D) ln a split-plot design, the
(A) Obtain a valid estimate of the precision of whole plot
treatments is less as compared
erorvariance
to their precision if they were
(B) Reduce the experimentatenor tried in a randomised block
(C) Maketheexperimentfreefrom design.
any systematic influence of
74. Which of the following statements is
environment wrong in respect of CRD ?
(D) Enable to infer whether the (A) lt is recommended in situations
differences in the treatment where some units are likely to
means are actually more than be destroyed orfailto respond.
the sampling fl uctuations (B) lt provides the maximum
numberof degrees of freedom
72. For a resolvable BIBD with for estimating experimental
parameters r}, b, r, k and l.:
error.
(A) b>O+r-k (C) lt is suitable only for a large
(B) bso+k-r numberof treatments.
(C) b>o+k-1 (D) ltiscompletelyflexible, i.e., any
numberof treatments and any
(D) b>o+r-1
number of units per treatment
73. ldentiffthe inconectstatement : may be used.
(A) Split-plot is the appropriate 75. lf the total response values for
design when two sets of treatment combinations aobo, bo,
"1
treatments are involved in the ,obr and ,rbr in a iactoriat
experiment requiring large size experiment with 2 factors A and B
plots. each at 2 levels from 4 replications
are respectively 18,17,25 and 30,
(B) A split-plot design is a
find the sum of squares for the
confounded design in which the
interaction effectAB :
main plot treatments are
confounded.
(A) 1.35
(C) ln a split-plot design, increased (B) 2.25
precision is attained on subplot (c) 2.50
treatments and interaction. (D) 1.00
tw- 18/9 (17 ) ( Tum over )
Text of page 18
76. Consider a RBD for t treatments and 78. ln a k x k Latin Square design one
observation is missing and suppose
rblockswith Sfr and 52=asthe mean
that R, C aM T aretotals ofthe known
squares due to block and enor. Then observations of row, column and
the efficiency of this design relative treatment containing the missing
vatue, and G is the total of (k2 - 1)
to CRD, if conducted for the same available values. The estimated
experiment, is: value of the missing observation is:
I
r(t-1)Sfl +(r-1)S2s
(k-1XR+c+r)-c
(A)
(A) (r-r)(r-z)
(rt - t)s2s
k(R+c+r)-2c
(B)
. r(t-1)se (B)
(r-r)(r-z)
1+
(rr-1)st-
(r -r)(t- r)s! + (r - r) s2s
(r-t)(n+c+ -2G
(c)
(c)
(rt-t)s[ 1
(rt-l)sfl +(r-t)sfr
k(R+c+T)-c
(D) 2
(D) k
(rt-l)sa 1
79. Consider a 23 partially confounded
77. lf interaction AC is confounded in a
design involving 3 factors A, B and
23 factorial experiment with factors
C with 4 replicates and 5 such
A, B and C, the arrangement of the
repetitions. lf the interactions AB, AC,
treatment combinations for two BC and ABC are partially
blocks in a replicate will be : confounded ea0h with 5 repetitions,
(A) Block 1 : b, ac, bc, a the degrees of freedom forthe error
Block 2: (1), ab, c, abc willbe :
(B) Block 1 : b, c, ab, ac (A) 15e
Block 2: (1\, a, bc, abc
(C) Block 1 : (1), ab, ac, bc (B) 3s
Block 2: a,b, c, abc (c) 113
(D) Block 1 '. a, c, bc, ab
Block 2: (1), ac, b, abc
(D) 28
tw- 18/9 (18) Contd
Text of page 19
80. A strip-plot experiment is conducted 83. From a data set consisting of
with 5levels of irrigation and 4levels defective items for40 samples each
of an insecticide for foliar spray. The of size 50, the average fraction
experiment contained 3 replications.
defective is calculated as 0.10. The
The errordegrees of freedom forthe
upper and lower control limits for the
interaction effect will be :
p-chart are respectively :
(A) 24
(A) 0.23,- 0.04
(B) 1e
(B) 0.13, - 0.04
(c) 22
(D) 30
(c) 0.35, - 0.03
(D) 0.23, - 0.03
81. The control chart suitable for the
number of bubbles observed per 84. R-charts are genbrally used :
square meter in a sheet of glass is : (A) To improve the quality of
(A) R-chart individual units of production
(B) C-chart (B) To know basic variability of
(C) p+hart q uality cl"iaracteristics
(D) X-chart (C) To help in reducing the average
82. Some points beyond the control fraction defectives
limits on the both sides in the (D) To showthe random variation
I-chart indicates that : in quality of lots which are
(A) The process level is gradually produced for inspection
changing
85. The control chart used to monitor
(B) There issystematicdifferences
' within the samples
attributes is
(C) The variability in the quali$ has (A) Range chart
been increased
-.
(B) Mean chart
(D) The level of the process has (C) Chartfornumberofdefects
been shifted (D) Chartforfractiondefectives
tw- 18/9 (1e) (Tum over)
Text of page 20
86 Acceptance sampling is not used (D) As OC curve represents some
when risk factors, the protection
(A) The test is destructive afforded to the consumer by
various sampling plans may be
(B) The cost of 100% inspection is
compared by examining their
quite high
OC curves
(C) The supplier's process
capability is very high 89. For a single sampling plan with lot
(D) Although the supplier process size 500, sample size 50,
acceptance number 3 and probability
is satisfactory but a program is
of acceptance 0.90, computeA.T.l. :
needed for continuous
monitoring
(A) e5
(B) 455
87. The maximum value of the average (c) 175
outgoing quality overall possible
(D). 505
values of the proportion defective is
called: 90. ln a double sampling plan, n, and n,
(A) Acceptabte quality level are respectively sizes of the first and
second samples. lf P., and Prare
(B) Average outgoing quality limit
respectively probabilities of decision
(C) Average outgoing quality level on the basis of first and second
(D) Lottoleraneprotediondefec{ive samples, the expected sample size
fortaking a decision is :
88. Which of the following statement is
nottrue regarding the OC curve ?
(A) ASN = nrPr * (n, + nr)P,
(A) The OC curve plots the (B) ASN = nrPr * (n., + nr)(1 - Pr)
probability of accepting the lot (C) ASN = nrPr * nr(1-Pr)
for a range of proportion of (D) ASN = nr(1 - Pr) + (n., + nr)P.,
defective items 91. Which of the following cross
(B) ln an ideal OC curve, the validation techniques is better suited
probability of acceptance of a forthe time series data ?
lot having proportion of (A) k-fold cross validation
* defectives less than or equal to (B) Leave-one-outcrossvalidation
LTPD value is equalto unity
(C) Stratified shuffle split cross
(C) A sample size and an validation
acceptance number are (D) Forward chaining cross
required to draw an OC curve validation
!
!w- 18/9 (20) Contd
Text of page 21
92. ln the theory of time series, shortage 96. Ratio to trend method for studying
of certain consumer goods before seasonal variation yields better
the annual budget of the country is resultswhen:
due to : (A) The periodsareof long duration
(A) Seasonalvariation (B) Seasonal variation is not a
(B) Seculartrend constant factor of trend value
(C) lrregularvariation (C) Cyclical variations are either
(D) Cyclicalvariation present or if present not so
93. Sirnple average method for finding significant
out seasonal indices is good when (D) Trend is linear
the time series :
97. lt is desired to determine a trend
(A) lsfreefrom trend curve in a time series by a moving
(B) Has no cyclic effect avemge covering consecutive sets of
(C) Has no trend and cyclical points (U_2, U_t, Uo, Ul, Ur) and
variation suppose we regard a quadratic
(D) Has allcomponents potynomial as.providing a satisfactory
approximation. What would be the
94. The moving averages in a time-
trend vatue ?
series can be made free from the
influences of :
(A) + 12n-,t+ 17Uo +
(A) Seasonal and cyclic variations $t-au-,
(B) Seasonalandinegularvariations
12U
f 3U2) .
1
(C) Trend and cyclicalvariations (B) 111Us +
Zlezu_za7Ut
(D) Trend and random variations 7U
1-2U2)
95. The equation U, = crglrepresents a :
(c)
1
6U_r a 15Us +
21e3U_2..
(A) Logistic curve 6Ul - 3U2)
(B) Modifiedexponentialcurve 1
(C) Exponentialcurve (D) * 4U-r ,,' 11Us +
1Se2U_z
(D) Gompertzcurve 4U1-2U2)
lw- 18/9 (21\ (Tum over)
Text of page 22
98. Examine critically the following (B) Trend can be eliminated by
statements and identify the wrong
applying corrections only if the
one:
growth is of constantamountor
(A) Harmon ic analysis decomposes
constant rate I
a periodictime series data into
sum of sinusoidal functions (C) Theactualcalculationsinvolved
(B) Harmonic analysis for studying more complicated
cyclical variation in the time (D) Utilizes data more completely
series mainly utilizes Taylor
series 100. Which of the following statement is
(c) To avoid huge calculations, not correct regarding the variate
harmonic analysis may be difference method ?
carried out with some trial
(A) The vafidnce of the random
periods of oscillation guessed
component can be estimated
from the graph of the series
bythis method
(D) Harmonic analysis is used to
estimate phase and amplitude (B) It can measure the random
of the cyclical variation component when the trend of
99. As compared to the ratio to moving the time series is smooth
average method, which of the (c) It is not suitabte if there are
following statement is wrong forthe
oscillations in the given series
link relatives method of studying
(D) It can determine the degree of
seasonalvariations ?
(A) The average of link relatives the polynomialwith which the
contains both trend and cyclica! trend of the series can be
-
components represented
{F
IIITITIIITTTTII
!w- 18/9 (22) Contd
Text of page 23
SPACE FOR ROUGH WORK IW- 18/9 (23) (Tum over)
Text of page 24
SPACE FOR ROUGH WORK
I
J
lII
a
I
rw-18t9(270) (24) StatisticsOfficial key not published for this paper.
Page 1 of 24
Source: State Selection Board. Question paper published by State Selection Board.