Statistical Inference MCQs with Answers | Statistics – Page 2

Question 21 Statistical Inference

To perform a runs test for randomness, the data must be?

Correct answer C. Divided into exactly two classifications

Open question

Question 22 Statistical Inference

What does Spearman’s rank correlation test require of the data?

Correct answer B. Data should be of ordinal scale at least

Open question

Question 23 Statistical Inference

In a Wilcoxon rank-sum test, which statement about ties is correct?

Correct answer A. Ties between the two samples may affect the decision

Open question

Question 24 Statistical Inference

In the sign test, what is done when the two scores in a pair are tied?

Correct answer C. We discard them

Open question

Question 25 Statistical Inference

A Wilcoxon rank-sum test can be?

Correct answer A. Either of the above

Open question

Question 26 Statistical Inference

Which of the following tests are based on rank sums?

Correct answer D. Kruskal-Wallis and Wilcoxon tests

Open question

Question 27 Statistical Inference

If f(x1, x2, …, xn; θ) = g(θ̂; θ) h(x1, x2, …, xn), then θ̂ is?

Correct answer C. Sufficient

Open question

Question 28 Statistical Inference

If Var(θ̂) → 0 as n → ∞, then θ̂ is said to be?

Correct answer A. Consistent

Open question

Question 29 Statistical Inference

Let X1, X2, …, Xn be a random sample from f(x; θ). If the conditional distribution of X1, …, Xn given S = s does not depend on θ for any value s, the statistic S is called?

Correct answer B. Sufficient statistic

Open question

Question 30 Statistical Inference

For a biased estimator θ̂ of θ, which relation is correct?

Correct answer D. MSE(θ̂) = Var(θ̂) + Bias²

Open question

Question 31 Statistical Inference

A set of jointly sufficient statistics is minimal sufficient if and only if?

Correct answer C. It is a function of every other set of sufficient statistics

Open question

Question 32 Statistical Inference

If, for every value s, the conditional distribution of X1, X2, …, Xn given S = s does not depend on θ, the statistic S = s(X1, …, Xn) is called?

Correct answer D. Sufficient

Open question

Question 33 Statistical Inference

A test is called the most powerful test of size α if?

Correct answer B. Among all other tests of size α or less, it has the largest power

Open question

Question 34 Statistical Inference

For two estimators T1 = t1(X1, …, Xn) and T2 = t2(X1, …, Xn), what is t1 called if its risk satisfies Rt1(θ) ≤ Rt2(θ) for all θ in Θ?

Correct answer A. Admissible estimator

Open question

Question 35 Statistical Inference

For two unbiased estimators T1 and T2, if Var(T1) < Var(T2), then T1 is said to be more?

Correct answer B. Efficient

Open question

Question 36 Statistical Inference

If E(θ̂) = θ, then θ̂ is said to be?

Correct answer B. Unbiased

Open question

Question 37 Statistical Inference

Let X1, …, Xn be a random sample from f(x | θ), where θ is a value of a random variable Θ with known prior density gΘ(θ). The estimator of τ(θ) defined as E is called the?

Correct answer A. Posterior Bayes estimator

Open question

Question 38 Statistical Inference

The sample proportion p is what kind of estimator of the population proportion?

Correct answer B. Unbiased

Open question

Question 39 Statistical Inference

The sample variance S² (divisor n − 1) is an unbiased estimator of the population variance σ² because?

Correct answer B. E(S²) = σ²

Open question

Question 40 Statistical Inference

A sample mean of x̄ = 40 is an estimate of?

Correct answer D. μ

Open question