Box 1 contains 100 tickets labeled with numbers, and Box 2 contains 1,000 ticket

Question

Box 1 contains 100 tickets labeled with numbers, and Box 2 contains 1,000 tickets labeled with numbers. The average of the labels on the tickets in Box 1 is 31 with an SD of 8. The average of the labels on the tickets in Box 2 is 43 with an SD of 15.

Q1) The normal approximation to the distribution of the sample sum of 10 independent random draws with replacement from Box 1 is

A: less accurate than

B: of the same accuracy as

C: more accurate than

D: could be less, equally, or more accurate than  

the normal approximation to the distribution of the sample sum of 10 independent random draws with replacement from Box 2.

Q2) The normal approximation to the distribution of the sample sum of 10 independent random draws with replacement from Box 1 is

A: less accurate than

B: of the same accuracy as

C: more accurate than

D: could be less, equally, or more accurate than  

the normal approximation to the distribution of the sample sum of 100 independent random draws with replacement from Box 2.

Explanation / Answer

The normal approximation to the distribution of the sample sum of 10 independent random draws with replacement from Box 1 is

C. More accurate than the normal approximation of the distribution of the sample sum of 10 independent random draws with relreplacem from Box 2

Because SD of box 1 is having smaller SD than box 2

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