Statistics MCQs

Page No. 34

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


a E(S2) = s2

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bE(u) = X

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cE(P) = P

✓


dUx = u

✖


View Answer E(P) = P

Sample proportion P is __________ estimator?


aBiased

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bParameter

✖


cUnbiased

✓


dNone of these

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View Answer Unbiased

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


aE(x) = µ

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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

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cBay’s estimator

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dSufficient estimator

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


aUnbiased

✓


bConsistent

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cSufficient

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dEfficient

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View Answer Unbiased

if Var(T2)_______________?


aEfficient

✓


bSufficient

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cUnbiased

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dConsistent

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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

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bAdmissible estimator

✓


cSufficient estimator

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dMinimax estimator

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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

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

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

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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

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bSufficient

✓


cConsistent

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dEfficient

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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.

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bIt is a function of every other set of sufficient

✓


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

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

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