Two designs to obtain estimates

The weights of three individual objects are to be estimated. Two different designs to obtain these estimates are being considered:

D1:

The three objects are weighed individually, seven times each.

D2:

i. Each object is weighed separately once.

ii. Then the objects are weighed two at a time in the three possible, different combinations.

iii. Finally, the three objects are weighed all together, once.

iv. This factorial design (steps i, ii, and iii) is repeated three times.

The two designs both use all of the n = 21 measurements for which funds are available.

Which design do you EXPECT to yield the more precise estimates of the individual weights of the three objects? Why? Show the details of your work.

What assumptions does your answer require?

Note: To answer this question you do no need to know, or use, the "y" values; nor do you need to estimate the residual mean squares.

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