Start practising

Subject / 721 questions

Statistics MCQs

Page 5 of Statistics multiple-choice questions with answers. Tap an option to check yourself.

Page 5 of 37

Question 81 Statistical Inference

Which of the following tests are based on rank sums?

Correct answer D. Kruskal-Wallis and Wilcoxon tests

Open question

Question 82 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 83 Statistical Inference

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

Correct answer A. Consistent

Open question

Advertisement

Question 84 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 85 Statistical Inference

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

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

Open question

Question 86 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 87 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 88 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 89 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

Advertisement

Question 90 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 91 Statistical Inference

If E(θ̂) = θ, then θ̂ is said to be?

Correct answer B. Unbiased

Open question

Question 92 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 93 Statistical Inference

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

Correct answer B. Unbiased

Open question

Question 94 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 95 Statistical Inference

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

Correct answer D. μ

Open question

Advertisement

Question 96 Statistical Inference

What is an estimate expressed by a single value called?

Correct answer B. Point estimate

Open question

Question 97 Statistical Inference

What are the 95% confidence limits for the population mean μ?

Correct answer B. x̄ ± 1.96 σ/√n

Open question

Question 98 Statistical Inference

What is E(x̄1 − x̄2)?

Correct answer D. μ1 − μ2

Open question

Question 99 Statistical Inference

Which of these is an example of a simple hypothesis?

Correct answer C. u = 20

Open question

Question 100 Statistical Inference

If n = 400 and p = 0.69, what is the 90% confidence interval for P?

Correct answer C. 0.652 and 0.728

Open question