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Chapter 2: Problem 14

Suppose that a group of 1000 orange trees is laid out in 40 rows of 25 trees each. To determine the sugar content of fruit from a sample of 30 trees, researcher \(A\) suggests randomly selecting five rows and then randomly selecting six trees from each sampled row. Researcher \(\mathrm{B}\) suggests numbering each tree on a map of the trees from 1 to 1000 and using random numbers to select 30 of the trees. Which selection method is preferred? Explain.

Short Answer

Expert verified
Researcher B's method is preferred because it provides the most unbiased and representative sample of the tree population.

Step by step solution

01

Analyze Researcher A鈥檚 method

In Researcher A's method, the trees are not chosen completely at random, because the trees' location (in the same row) can affect the trees' selection. As a result, only six trees from each of five rows are chosen. If for some reason sugar levels vary by row (for example, due to differences in sunlight, water, or soil conditions), this method would not catch that variation.
02

Analyze Researcher B鈥檚 method

In Researcher B's method, every tree has an equal chance of being selected, which means it is a simple random sample. This method doesn't factor in the trees' locations and thus might eliminate potential sources of bias.
03

Compare both methods

Comparing both methods, it is clear that Researcher B's method allows for a more representative and unbiased sample. This is because it gives a fair chance for every tree in the plantation to be chosen as a part of the sample, regardless of its location.

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