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.