61.
"Simple
random sampling" is the technique of drawing a sample in such a way that
each unit of the population has

(A)
distinct and dependent chance of being included in the sample

(B)
distinct but independent chance of being included in the sample

(C)
an equal but dependent chance of being included in the sample

(D)
an equal and independent chance of being included in the sample

Answer: D

62.
In
SRSWR with usual notations, the standard error of the sample mean `quadbary` is

(A)
`quadS({N-n}/{Nn})^{1/2}`

(B)
`quadS({N-1}/{Nn})^{1/2}`

(C)
`quadS(1-{n}/{N})^{1/2}`

(D)
`quadS/n(1-{1}/{N})^{1/2}`

Answer: B

63.
The
formulae for optimum allocation in various strata in stratified sampling were
first derived by

(A)
Tschuprov

(B)
Cochran

(C)
Lahiri

(D)
Neymann

Answer: A

64.
The
ratio estimator of population mean is unbiased if sampling is done according to

(A)
PPSWR

(B)
PPSWOR

(C)
SRSWR

(D)
SRSWOR

Answer: A

65.
The
cluster sampling is more efficient when

(A)
the variation within clusters in more

(B)
the variation between clusters is less

(C)
both (A) and (B)

(D)
neither (A) nor (B)

Answer: C

66.
Local
control is a device to maintain

(A)
homogeneity within blocks

(B)
homogeneity among blocks

(C)
both (A) and (B)

(D)
neither (A) nor (B)

Answer: A

67.
In
a linear model `quadY_{ij}=alpha_i+e_{ij},` `quadj=1,2,...,n_i;`
`quadi=1,2,...,k,` consider

(i)
`quadalpha_1-3alpha_2+alpha_3+alpha_4`

(ii)
`quadalpha_1+3alpha_2-alpha_3-alpha_4`

(iii)
`quadalpha_1+3alpha_2-2alpha_3-2alpha_4`

Then
which of the following is correct?

(A)
(i) and (ii) are linear contrasts

(B)
(i) and (iii) are linear contrasts

(C)
(ii) and (iii) are linear contrasts

(D)
(i), (ii) and (iii) are linear contrasts

Answer: B

68.
While
analyzing the data of a `quadkxxk` Latin Square Design, the degrees of freedom
in the ANOVA is

(A)
`quadk^2-1`

(B)
`quadk-1`

(C)
`quadk^2-2k+1`

(D)
`quad(k-1)(k-2)`

Answer: D

69.
In
a split plot design with factor `quadA` at 3 levels in main plots, factor
`quadB` at 3 levels in sub-plots and 3 replications, the degrees of freedom for
sub-plot error is

(A)
27

(B)
12

(C)
8

(D)
4

Answer: B

70.
If
the interactions `quadAB` and `quadBC` are confounded with incomplete blocks in
a `quad2^n` factorial experiment, then automatically confounded effect is

(A)
`quadA`

(B)
`quadC`

(C)
`quadAC`

(D)
`quadABC`

Answer: C

71.
Which
among the following is a consistent estimator of the population mean when
samples are from the Cauchy population?

(A)
Sample mean

(B)
Sample median

(C)
Sample variance

(D)
None of these

Answer: B

72.
If
the regularity conditions of the CR inequality are violated then the least
attainable variance will be

(A)
equal to the CR bound

(B)
greater than the CR bound

(C)
less than the CR bound

(D)
zero

Answer: C

73.
A
method to obtain the UMVUE is by using

(A)
Rao-Blackwell Theorem

(B)
Baye's Theorem

(C)
Neymann-Pearson Theorem

(D)
Lehmann-Scheffe Theorem

Answer: D

74.
A
complete-sufficient statistic for `p` in the Bernoulli distribution

`(x,
p) = p^x (1-p)^x; x=0, 1.

=
0 `"otherwise"` is

(A)
The first order statistic `X_{(1)}`

(B)
The `n` `"^{th}"` order statistic `X_{(n)}`

(C)
`sum_(i=1)^n X_i`

(D)
`X_{(n)}-X_{(1)}`

Answer: C

75.
The
least square estimators are

(A)
Unbiased

(B)
BLUE

(C)
UMVUE

(D)
All these

Answer: D

76.
A
95% confidence interval for λ, when a large sample is taken from a Poisson
population with parameter λ is

(A)
`bar x ``+- 1.65``sqrt(( bar x)/(n)) `

(B)
`lambda+- 1.65 sqrt((lambda)/(n)) `

(C)
`bar x+- 1.96sqrt((bar x)/(n)) `

(D)
`lambda +- 1.96sqrt((lambda)/(n)) `

Answer: C

77.
The
minimum Chi-squared estimators are not necessarily

(A)
Unbiased

(B)
Consistent

(C)
Efficient

(D)
Asymptotically normal

Answer: A

78.
Which
one of the following statements is true?

(A)
Even if the UMP test does not exist, a UMPU test may exist

(B)
Even if the UMPU test does not exist, a UMP test may exist

(C)
A UMP test exists only if a UMPU test exists

(D)
A UMPU test exists only if a UMP test exists

Answer: A

79.
In
paired `t` test the two random variables should be

(A)
Paired and uncorrelated

(B)
Unpaired and correlated

(C)
Both paired and correlated

(D)
Neither paired nor correlated

Answer: C

80.
With
usual notations, the criterion for acceptance in SPRT is

(A)
`lambda_m <= ((1-beta))/(alpha) `

(B)
`lambda_m >= ((1-beta))/(alpha) `

(C)
`lambda_m <=(beta)/((1-alpha)) `

(D)
` lambda_m >= (beta)/((1-alpha)`

Answer: C

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