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Let ‏جلا . - . ,22 برلا‎ be a random sample from N(0, 42 ; 6 > 0. Which of the following testing

0
problems has the region ۳ நமி ER” 58 > [ | as the most powertul critical
டம
1

region of level ०, where > ५ denotes the upper ० quantile of a 7 distribution with n degrees of
freedom. ∎

A) Ho: ७2 =1 against 111 :62 = 2 8) Ho: ७2 = 2 against H, :02-4

©) Hp : 02 = 2 against H, : ०2 = 1 D) Hg: ०2 = 1 against Hy : 67 = 0.5

Let ‏جلا . - . ,22 رولا‎ be a random sample from f(x, 9) = ര, 0 0. For testing 110 : 05 00
against 111 : ۵< ‏,م6‎ a uniformly most powerful test of size o reject Ho if

A) X(q) > പാടില...) ‏ہت‎ ०,2५1) = Min (X4, Xp, +--+ Xq)
n 0

©) ]]× <0 , © constant 0) 2. X;>C, Caconstant
1 =

160, ‏بولا‎ - - - › X, be a random sample from a population having 0.6.1.

f(x, 0) = 86൦ 9× ‏ح×‎ 0, 6> 0. Totest 110 : 8 = 00 against H, : 6 > 60 the critical region of the likelihood
ratio testis of the form

A) ೫೬೦ 8) 2൦ ©) ‏ی×‎ <© 0) 24 >6

For the SPRT of strength (५, 0) which of the following inequalities is satisfied by the stopping bounds
^ 8५8 (^> 8(

In simple random sampling with replacement of fixed sample size n from a population of size N, the
probability that a particular unit is selected atleast once in a sample is

ய ய ய
^) [1-4 உடம்‌ 9 (4 0) ‏ل‎

N N N ‏ك۷‎
‎From a population of size 14, a sample of 5 units is to be selected by circular systematic sampling.
Let the first number selected at random be 7. Which other units are to be included in the sample ?
A) 7, 10, 13, 1, 4 8) 7, 11, 1, 5, 9 ©) 711, 1, 4, 8 D) 7, 10, 13, 2, 5
If p is the intra class correlation, then cluster sampling is more efficient than simple random sampling
when

A) p=0 8) 0>0 C) p=1 ഉ) 040
~ With usual notations, in simple random sampling, bias of the ratio estimator पि is given by
A x 1-1
A) ന ತು, 8) (c2 =pC,Cy)

©) -cov(R, x) D) 1