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1. Following is not the method of collecting primary data:

Direct Personal Interview


Indirect oral interview


.Using the schedule


Using Government Publications


2. Pie diagram is

One dimensional diagram


Two dimensional diagram


Three dimensional diagram


Pictogram


3. If the frequencies of variable values n are the terms of the binomial series P q respectively, then the arithmetic mean is
n np
npq cannot find
4. In any discrete distribution the relation between Standard Deviation and Mean Deviation from mean is

SO MD from mean


SO MD from mean


MD from mean


SO =MD from mean

S.
Ifeach of a series is divided by 5. its coefficient of Variati0n is reduced by





10% 20%


6. If one regression coefficient is greater than one, then second one must be
greater than 1 equal to 1
less than 1 no change
Serles·B 2 BAC·58

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22. If X and Yare two independent chi-square variates with vI and Vz dJ respectively, then F-statistics is defined by X X

Y
None of the above
23. F-distribution is applied for

testing the equality of two population variances


for testing the equality of two and more population means


for testing the equality of several regression coefficients


all the above


24. With vI the F-distribution implies

XZ -distribution with VzdJ


XZ -distribution with vz) dJ


t-distribution with VzdJ


t-distribution with dJ


z
25. If Xz, ....., XisarandomsamplefromapopulationN(Il,( 2),thesufficientstatisticfor
n
OZ is





none of the above


26. Bias of an estimator can be

positive negative


either positive or negative always zero


Series-B 6 BAC·58
27. Cramer -Rao inequality is valid in case of

continuous variables discrete variables


both and neither nor


28. Rao-Blackwell theorem enables us to obtain minimum variance unbiased estimator through

unbiased estimators complete statistics


efficient statistics sufficient statistics


29. If t is a consistent estimator of then

t is also a consistent estimator of e2


t2 is also a consistent estimator of e


t2 is also a consistent estimator of e2


none of the above


30. The credit of inventing the method of moments for estimating the parameters goes to

R. A. Fisher J. Neyman


Laplace Karl Pearson


31. Minimum chi-square estimators are

consistent asymptotically normal


efficient all the above


32. If X2, Xis a random sample from a population with p.d.f.
n

the maximum likelihuod estimator for ais Lx; In Lxf n
BAC-58 7 S...ic.-B

33. Least square theory was propounded by whom and in which year?

Gauss in 1809 Markov in 1900


Fisher in 1920 None of the above


34. Efficiency of sample mean as compared to median as an estimate of the mean of a normal population is

64% 157%


317% 31.5%


35. The diameter of cylindrical rods is assumed to be normally distributed with a variance of
0.04 em. A sample of 25 rods has a mean diameter of 4.5 ems. 95% confidence limits for population mean are

4.5 ± 0.004 4.5 ± 0.0016


4.5 ± 0.078 4.5 ± 0.2


36. If the density function of a variable X is
8 e-llx for 0
95% central confidence limits for large sample n are


± x

l±V;;J
none of the above
37. Formula for 95% confidence limits for the variance of population when J.! is unknown is given by
ns2


2
X (0.025) X (0.975)
ns2 ns2

2 2
X 0.Q25 X 0.975
2X 0.025
ns2 2X n,0.025
Serles·B

2
X 0.975
ns2
2

X n,0.975
8 BAC-58
38. The idea of testing of hypothesis was first set forth by

R. A. Fisher J. Neyman


E. L. Lehman A. Wald


39. Area of the critical region depends on

size of type I error


size of type IT error


value of the statistic


number of observations


40. Neyman-Pearson lemma provides

an unbiased test a most powerful test


an admissible test minimax test


41. In sequential probability ratio test, the sample size is

fixed fixed but small


fixed but large a random variable


42. An exact test for testing the independence of attributes in a contingency table of order x was given by

Karl Pearson Pascal


Demoivre R. A. Fisher


43. The X2 -statistic to test cr2 is based on a sample of size n has degrees of freedom equal to
n-1 n
n+1 none of the above
44. If in Wilcoxon's signed rank test, the sample size is large, the statistic is distributed with mean
n n(n



4 2
n (2n






4 4
BAC·58 9 Series-B
45. If there are 10 symbols of two types, equal in number, the maximum possible number of runs is

8 9


10


46. If the sample size in Wald-Wolfowitz runs test is large, the variate R is distributed with variance

n)2
mn (2mn


47. Reduction in the size of a test results into

decrease in its power


increase in its power


no change in its power


all the above


48. If two samples of size 9 and 11 have means 6.8 and 8.8 and variances 36 and 25
respectively from two populations and the absolute value of the statistic t for testing Ho: is

0.148 1.83


0.81 0.91


49. Assume that the daily sales of petrol follows exponential distribution. The hypothesis Ho that the sales of petrol is 1000 litres per day is tested against HI that it is 1500 litres per day. If the sales on a day is 1200 litres or more, flo is rejected, the size of type I error is
e-1.2 el.2
e-1.2 none of the above
Serles·B 10 HAC·58

50. In determining the average life length of bulbs produced by a company, one has the following Assertion and a Reason. Assertion A complete enumeration survey is to be performed.
Reason Average life length should be measured accurately as far as possible. Then choose the correct option from the following:

Both and are true and is the correct explanation for


Both and are true, but is not the correct explanation.


is true, but is false.


is false, but is true.


51. From a population containing 45 units, a simple random sample without replacement of five units are to be selected. The two digit random numbers to be used for the selection are the following:
40,52,85,18,38,77,98,48,83,56,92,31,40.
Then the sampling units are

18,38,77,98,48 40,52,85,18,38


18,38,32 40,18,38,31,40


52. Suppose a population consists of only 5 units with the values on a characteristic measured on them given by 2.1, 3.6, 4.2, 2.8, 2.3. Then what is the mean of all possible means of random samples (without replacement) of size two drawn from the above population?

3.00 2.85


3.15 2.20


53. In simple random sampling with replacement of three units from a population of N units, the probability that the sample contains all different units is equal to
(N

N3 N2
1 6

N(N N3
BAC·58 11 Series·B
54. Suppose one wish to estimate the population mean yo such that the probability of large
deviation of the sample mean y with yo exceeds d is equal to 0.05. Then the sample size required in simple random sampling is approximately equal to (for S2 to denote the mean square errors of the population).


0.05 e·96

SJ

0.95 d
0.95 e.96SJ



0.05 d



e·9; M1.9; Sf}




SJj{1+ Sf}
55. In simple random sampling, the variance of the sample proportion p of a characteristic with a corresponding population proportion P is equal to
P P

nN P P N-n

N n N-l
56. A population is divided into four stratas with strata size and strata variance for each strata given as below
Strata No. Strata Size Strata Variance
1 400 12.25
2 300 4.00
3 100 16.00
4 200 9.00

Then with the above information, for a stratified sample of size 90, the stratum sample size allocation are'

42, 18, 12, 18 36,27,9,18


25,15,30,20 23,23,22,22


Series-B 12 BAC-58
57. If VOpt' Vp'op and V,an are the variances of the mean due to stratified sampling under
optimum allocation, proponional allocation and random allocation respectively, then which of the· followi ng is correct?

Vopt:S; Vprop:S; V,an


Vprop:S; Vopt




58. If observations xi are measured on variables Y and X on each unit of a simple random n
sample of size then for f r=Y I X and large Var is approximately equal to


(Yj xl

N
i
(Yj xl



I
nX

59. Under simple random sampling, if f is the sampling fraction, then with usual notation,
the variance of the ratio estimator'; of the population mean Y is equal to R

N
L II
1

I N
I
±


n
1
n
L (y. _Rx.)2 11 I n

(Yi -Rxl
I-f

N
n i=I RAe-58 13 Series-R
60. In systematic sampling consider the following statements
A The sample mean of a linear systematic sample is always an unbiased estimator of population mean.
The sample mean of a circular systematic sample is an unbiased estimator of the population mean.
Then which of the following is correct?

Both A and B Neither A nor B


Only A Only B


61. Given the systematic sample mean with k the sampling interval, Pc the intraclass correlation between pairs of units within a sample. Now consider the following statements:

A Systematic sampling is more efficient than srs if Kn_ 1.

B Systematic sampling is less efficient than srs if Kn_ I

C Systematic sampling is as efficient as srs if Then which of the following is correct?




All Band C are true.


A is true but not Band C.


All B and C are false.


A and B are true but not C.



Kn_ I
62. In which of the following case cluster sampling is not preferred?

No reliable list of elements in the population is available.


It is prohibitively expensive to construct the list of elements in the population.


Economic considerations compels one to use larger cluster.


The list of elements is available, but there is large variability among the units of the population.


63. Which error of the following is called a sampling error?

Failure to measure some of the units in the survey.


Errors committed on the measurement of a unit.


Error occur in an estimate when only n of the units are measured instead of the complete population of N units.


Errors occur in editing, coding and tabulating the results.


Serles·B 14 BAC·58
64. In the one way analysis of variance model given by
Yij Uj Xij j ..,nij i ...., r

)CZ .Z i Z i
If Eyy= L Y. £." X. -and
ij IJ i OJ xx ij IJ i OJ
X.Y EXY )Cij 7,then to test Ho: b the statistic to be used is
r
IJ I
(usen=n l +nz ... EXyz/Exx EXYz
Eyy--
E
xx
EXYz 1

EXYZ)

n-r Eyy Exx
Exx
EXYz

I EXYZ)}
Eyy-Exx
Exx
65. The following is the layout and yields of an RBD with four blocks and 3 treatments of which one observation is missing (values given in parenthesis are yields)
Blocks Treatments
1 T3 Tz Tz
2 T1 T3
3 Tz T3 H T 1 7
4. T 1 Tz T3

Then the estimated value of the missing observation is
5.5 2
38/11 4 BAC·58 15 Series·B
66. The following is the arrangement of five treatments into 10 blocks: Block No.
Treatments
1

12 3
2

124
3

125
4

134
5

13 5
6

14 5
7

234
8

235
9

24 5
10

3 45
Then with usual notation the parameters of this design (BI BD) are







67. The standard error of difference between a pair of treatment means in a BmD is equal to
cr cr
_ill
cr "jIV cr
68. In confounding in 24 -factorial experiment, the intrablock subgroup of the confounding system is be, abd, acd}. Then the other blocks are

be, abed}, ac, abd, ab, acd, bd}





be, cd, abed, acd, bd}


ac, cd, abed}, ab, acd, bd}


69. If the principal block of the confounding system is as given in question Number 68, then the effects confounded are

ABC, BCD, AD AB, CD, ABCD


ACD, BC, ABD AC, BD, ABCD


Series-B 16 BAC-S8
70. If the principal block of the confounding system is as given in question No. 68 and if there are three repetitions of the same confounded arrangement, then the degrees of freedom for the error sum of squares in the ANOVA is equal to

36 32


30 24


71. In a split plot design with 3 main plot treatments, 4 sub plot treatments and 3 blocks, the sub plot error sum of squares has a degrees of freedom equal to

22 18


4 22


72. The error degrees of freedom in the Analysis of variance of the design given in question No. 66 is equal to
36 16
9 13
73. If the blocks of a 23-experiment are
be, ac, ab, ac,
ac, ab, ab,
abe} then the partially confounded effects are


AC, ABC


AB, ABC, BC


AB, BC, AC, ABC


AB, AC, BC


74. If the arrangement of treatments of a 23 -experiment in eight blocks are as given in question No. 73, then the error degrees of freedom in the analysis of the variance is given by

17 21


18 20


BAC·58 17 Serles·B
75. An experiment consists of flipping a coin and then flipping it a second time if a head occurs. If a tail occurs on the first flip, then a six faced die is tossed once. Then the total number of outcomes in the sample space is
2 6
8 12
76. From past experience it is known that an investor will invest in security A with a probability of 0.6, will invest in security B with a probability 0.3 and will invest in both A and B with a probability of 0.2. Then the probability that a customer will invest neither in A norin Bis

0.3 0.28


0.7 0.18


77. The probability that a student passes Mathematics is 4/9 and that he passes Physics is 2/5. Assuming that passing in Mathematics and Physics are independent of each other, what is the probability that he passes in Mathematics but fails in Physics?
19/45 8145
26/45 4/15
78. Two urns contain 6 white and 3 black balls and 5 white and 7 black ball respectively. An urn is chosen at random and a ball is drawn. It was found to be white. Then the probability that it was drawn from the first urn is,
8 1

13 3 55

12 24
79. An aircraft has three engines Band C. These engines work independent of each other. The aircraft fails if all the three engines fail. The probabilities of failure are 0.03, 0.02 and
0.05 for engines B and C respectively. What is the probability that the aircraft will not fail?
0...OO3 0.90
0.99997 0.90307
Series·B 18 BAC·58
SO. Certain discrete random variable X has the following probability mass function (p.mJ.)
x 0 1 2
P(X 1/16 3/16 4/16 3/16 3/16 1/16

Then Var(X) is
49

2
256
7 463

25616
81. The life of an electronic component is known to have the following probability density function (p.d.f.)
0.2e-Q·2x x 0
Then Var is


0.04 25


5 0.02


82. A random variable X has the following probability mass function
x
15 x
ThenE(X! x is equal to

45/14 3


45 15/14


83. A random variable X has the following distribution
I
12 0 x 12
o otherwise
Then P(5 X 71 x

3/4 1/4
2/3 1/6 BAC·58 19 Series-B
84. The probability distribution of a random variable X is given by X 5/2
o otherwise
Then the value of C is

25/24 2/15
24/25 Cd) 3/4
85. The probability distribution of a random variable X is given by
x12
41 x 0
Then is

2 1/2


4 1/4


86. A random variable X has uniform distribution over 1).
IfP{ IX- V21 a then using Chebychev's inequality the value of is

1/4 2/3


1/3 3/4


87. Let have a joint distribution given by 1. Then the conditional distribution of X given Y is

f(xIY)


f(xIY)


f(xIY)


f(xIY)


88. Among the following statements, which statement is true

Every sequence lx.,l of random variables obeys SILN.


Every sequence lx.,l of independent random variables obeys SILN.


Every sequence of i.i.d random variables with finite mean obeys SILN.


Every sequence of independent random variables with uniformly bounded


n
variance obeys SILN. Serles-B 20 BAC-S8
89. If X is binomial with parameters nand p and if P(X P 5). then
n 8
n= 10 n=9
90. A wall measures 40 m by 30 m contains a window of size 15 m by 10 m. The wall is hit by four stones thrown up by a mower. Assuming that each stone hits the wall in a random position independently of other stones, what is the probability that every throw hits the window?
1/8 114096
1/512
91. .Certain event occurs in accordance with Poisson distribution at the rate of 2 per hour. Then the probability that exactly one event will occur in two hours is
4e-4 e-2
e-2

0.04 2
2
92. The moment generating function M.O.F. of a LV. X is Then which one of the following statements is true?

Var


X has a Cauchy distribution



E =Var


=Var


1
93. The characteristic function of a random variable X is -12 . Then X has the following

distribution:


Laplace Cauchy


Exponential Uniform


94. A random variable X has uniform distribution over 2). Then the v
1/3 213
1/12 1
BAe-58 21 Series·B
95. A random variable Y has a normal distribution. Then the distribution of eY is

Exponential Laplace


Lognormal Weibul


96. An electronic signal hits at a counter. The signal may register or may miss. The probability that the signal registers in any hit is 0.25. Then the expected number of hits required for the signal to register is
5 4

97. If X and Y are Gamma variates, then x/Y is

Gamma variate Beta variate


Cauchy variate Chi-square variate


98. Identify the odd item in the following list:

Exponential distribution


Gamma distribution


Uniform distribution


Normal distribution


99. Let have a bivariate normal distribution. Then which one of the following statements is not true?

Marginal distributions of X and Yare normal.


Conditional distribution X given Y is normal.


X-Yisnormal.


X and Y are independent when p 1


100. Head of a row in Tabular presentation is called

Stub Caption


Title Foot note


Series·B 22 BAC-58
Space For Rough Work
BAC·S8 23 Serles·B