Statistics MCQs

Page No. 34

Sample variance S2 is unbiased estimator of population variance 26 because ________________?


a E(S2) = s2


bE(u) = X


cE(P) = P


dUx = u


View Answer E(P) = P

Sample proportion P is __________ estimator?


aBiased


bParameter


cUnbiased


dNone of these


View Answer Unbiased

An estimator Q is an unbiased estimator of the population parameter Q if ___________________?


aE(x) = µ


bE(Q) =Q


cE(Q) =Q


dE(P) = P


View Answer E(Q) =Q

Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the prior gΘ(θ) is define as_________________E[∏(θ)ιX1,X2,…..,Xn] is called?


aPosterior Bay’s estimator


bMinimax estimator


cBay’s estimator


dSufficient estimator



If E(θˆ)=θ, then θˆ is said to be_______________?


aUnbiased


bConsistent


cSufficient


dEfficient


View Answer Unbiased

if Var(T2)_______________?


aEfficient


bSufficient


cUnbiased


dConsistent


View Answer Efficient

for two estimators T1=t1(X1,X2,….Xn) and T1=t1(X1,X2,….Xn) then estimators t1 is defined to be Rt1(θ)≤Rt2(θ) for all θ in Θ ?


aConsistent estimator


bAdmissible estimator


cSufficient estimator


dMinimax estimator


View Answer Admissible estimator

A test is said to be most powerful test of size α, if_______________?


a Among all other test of size α or less it has the largest power


bAmong all other test of size α or greater it has the largest 1 – α


cAmong all other test of size α or greater it has the smallest power


d Among all other test of size α or greater it has the largest β



If the conditional distribution of X1,X2,…..Xn given S=s, does not depends on θ, for any value of S=s the statistics S=s(X1,X2,…..Xn) is called______________?


aUnbiased


bSufficient


cConsistent


dEfficient


View Answer Sufficient

A set of jointly sufficient statistic is defined to be minimal sufficient if and only if_______________?


aIt is a function of some other set of sufficient statistics.


bIt is a function of every other set of sufficient


cIt is a function of any sufficient statistics in the set.


d It is not a function of every other set of sufficient statistics.



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