SSC CGL Practice Quiz

Question 1

Let X1, X2, ..., Xn be a random sample from a population with mean μ and variance σ². Which of the following is always an unbiased estimator of μ?

Accepted Answer

Sample mean X̄

Question 2

An estimator T of parameter θ is called consistent if

Accepted Answer

T converges in probability to θ as n → ∞

Question 3

Let X1, X2, ..., Xn be a random sample from Bernoulli(p). Which estimator attains the Cramér–Rao lower bound for p?

Accepted Answer

Sample proportion p̂ = X̄

Question 4

A random sample X1, X2, ..., Xn is drawn from the density f(x;θ) = θx^(θ-1), 0 < x < 1, θ > 0. The maximum likelihood estimator of θ is

Accepted Answer

θ̂ = -n / ΣlnXi

Question 5

A random sample of size 16 is drawn from a normal population with unknown variance. To test H0: μ = μ0 against H1: μ ≠ μ0, the appropriate test statistic is

Accepted Answer

t = (X̄ - μ0)/(S/√n)

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