Statistical Inference and Hypothesis Testing-Characteristics of Good Estimator (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 16 - 20 of 54

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Question number: 16

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

Let X1,X2,X3 be a random sample of size n = 3 from a distribution with mean μ and variance σ2 . Then T=X1+X2X3 is a unbiased estimator of

Choices

Choice (4) Response

a.

3μ

b.

μ1

c.

μ+1

d.

None of the above

Question number: 17

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

An estimator T=x1,x2,.,xn is said to be sufficient for a parameter, if it contains

Choices

Choice (4) Response

a.

If the conditional distribution of x1,x2,.,xn , given T is independent of the parameter.

b.

All the information in the sample regarding the parameter.

c.

Both a. and b. are correct

d.

None of the above

Question number: 18

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

A random sample X1,X2,X3,X4,X5 of size 5 is drawn from a normal population with unknown mean μ . Then T1=2X1+X23 is a unbiased estimator of

Choices

Choice (4) Response

a.

2μ

b.

μ1

c.

μ

d.

3μ+1

Question number: 19

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If E(T)=θ , then which of the following is true?

Choices

Choice (4) Response

a.

T2 is a Unbiased estimator θ2

b.

T2 is a biased estimator of θ2

c.

E(T2)=θ2

d.

Question does not provide sufficient data or is vague

Question number: 20

» Statistical Inference and Hypothesis Testing » Characteristics of Good Estimator

MCQ▾

Question

If the mean of the estimator is not equal to the population parameter, the estimator is said to be:

Choices

Choice (4) Response

a.

Biased

b.

Positively biased

c.

Unbiased

d.

Negatively biased

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