It is generally reasonable to use the entire population instead of a sample when the population is small or easily accessible. In the scenarios provided:
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A scientist wants to determine the average age of the trees in a national forest. - Likely not reasonable, as national forests can have a large number of trees, making it impractical to measure every tree.
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A teacher wants to know his students’ favorite holiday in all of his math classes. - This is reasonable if "all of his math classes" refers to a manageable number of students. If it’s just his classes, he can easily survey all of them.
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A store manager wants to know the percentage of customers who prefer cold coffee over hot coffee. - Not reasonable, as customers can be numerous and varied, making it difficult to gather data from the entire customer base.
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A university dean wants to estimate the number of students who work and study at the same time. - Not reasonable since the student population could be very large and diverse.
Based on the explanations, the most reasonable situation to use the entire population is the second one: A teacher wants to know his students’ favorite holiday in all of his math classes.
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