Question

Researchers A and B each have a random sample from the same population, which has mean and a finite variance. Here are their data:

Researcher A Researcher B

Sample sizes
n_{A}
n_{B}

Sample means

Consider the following claims:

Claim 1. If n_{A} > n_{B}, the
estimator puts too much weight on researcher A’s
observations to be efficient.

Claim 2. If n_{A} ≠≠ n_{B}, the
estimator is biased.

Claim 3. If n_{A} > n_{B}, we can make the
estimator more efficient by increasing from ½
to .

Which of the following is your
answer? **LETTER.**

A. Claims 1 and 2 are FALSE, claim 3 is TRUE.

B. Claims 1 and 3 are TRUE, claim 2 is FALSE.

C. Claims 2 and 3 are TRUE, claim 1 is FALSE.

D. All three claims are TRUE.

E. All three claims are FALSE.

Answer #1

Researchers A and B each have a random sample from the same population, which has mean and a finite variance. Here are their data:

Researcher A Researcher B

Sample sizes nA nB

Sample means

Consider the following claims:

Claim 1. If nA > nB, the estimator puts too much weight on researcher A’s observations to be efficient.

Claim 2. If nA ≠≠ nB, the estimator is biased.

Claim 3. If nA > nB, we can make the estimator more efficient by increasing from ½ to

Which of the following is your answer

the correct option is

B. Claims 1 and 3 are TRUE, claim 2 is FALSE.

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