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A circus owner is planning to ship his 50 elephants and needs a rough estimate of their total weight. He plans to estimate the weight by weighing just one elephant. Which one should he choose? This 1971 problem posed by Basu illustrates the problem of sampling inference. The author uses this fable as a basis for this introduction to the subject. He looks at the question of whether sampling inferences should be made primarily in terms of inclusion probabilities, or whether they should be based on estimates of the parameters of a realistic population model. He argues, using the fable of Basu’s elephants, that the two approaches are complementary – the former being more appropriate for large samples and the latter for small ones. The last half of the book covers populations other than elephants - from businesses, trees and households. |