Question at position 7 Identify the sample and the population: A maple sugar manufacturer wants to estimate the average trunk diameter of maple trees in a large forest. He divides the forest into several hundred 50-meter by 50-meter plots, selects 10 plots at random, and measures the diameter of every maple tree in each selected plot.The population is all maple trees in the large forest. The sample consists of the maple trees that are in the randomly selected plots.The population consists of the maple trees that are in the randomly selected plots. The sample is the several hundred 50-meter by 50-meter plots.The population is all maple trees in the large forest. The sample is the several hundred 50-meter by 50-meter plots.The population consists of the maple trees that are in the randomly selected plots. The sample is all maple trees in the large forest.Cannot be determined.

Question

Question at position 7 Identify the sample and the population: A maple sugar manufacturer wants to estimate the average trunk diameter of maple trees in a large forest. He divides the forest into several hundred 50-meter by 50-meter plots, selects 10 plots at random, and measures the diameter of every maple tree in each selected plot.The population is all maple trees in the large forest. The sample consists of the maple trees that are in the randomly selected plots.The population consists of the maple trees that are in the randomly selected plots. The sample is the several hundred 50-meter by 50-meter plots.The population is all maple trees in the large forest. The sample is the several hundred 50-meter by 50-meter plots.The population consists of the maple trees that are in the randomly selected plots. The sample is all maple trees in the large forest.Cannot be determined.

BlackTom AI · Accepted Answer

Question restatement: A maple sugar manufacturer wants to estimate the average trunk diameter of maple trees in a large forest. He divides the forest into several hundred 50-meter by 50-meter plots, selects 10 plots at random, and measures the diameter of every maple tree in each selected plot. Identify the sample and the population.

Option A: The population is all maple trees in the large forest. The sample consists of the maple trees that are in the randomly selected plots.
- This aligns with the standard definitions: the population includes all maple trees in the forest, and the sample includes those trees within the 10 randomly selected plots. It correctly distinguishes between population (all trees) and sample (trees in the chosen plots).

Option B: The population consists of the maple trees that are in the randomly selected plots. The sample is the several hundred 50-meter by 50-meter plots.
- This confuses population and sample. The population is not limited to the trees in the plots; it should include all trees in the forest. The plots are units of observation, not the population itself.

Option C: The population is all maple trees in the large forest. The sample is the several hundred 50-meter by 50-meter plots.
- This reverses the roles. The sample cannot be the plots themselves since measurements are taken from trees, not the plots as whole units. The sample should be the trees measured, not the plots.

Option D: The population consists of the maple trees that are in the randomly selected plots. The sample is all maple trees in the large forest.
- This is inverted and incorrect. The population cannot be restricted to only the trees in the selected plots, and the sample cannot be the entire forest.

Option E: Cannot be determined.
- Given the description, the population and sample are clearly defined by the sampling design (trees in the forest vs. trees within the sampled plots), so this choice is unnecessary and incorrect.

Putting it together, the reasoning for each option emphasizes the fundamental sampling definitions: population = all members of interest, sample = subset actually measured. The correct pairing remains the population = all maple trees in the large forest, and the sample = the maple trees in the randomly selected plots, since measurements were taken from trees within those plots and not from the plots as whole units or from the forest as a whole without focusing on the selected plots.

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