Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland’s ancient high kings (Reference: Tara, An Archaeological Survey by Conor Newman, Royal Irish Academy, Dublin). Independent random samples from two regions in Tara gave the following phosphorous measurements (in ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.

Region I: x₁; n₁ = 12

Region I: x₂; n₂ = 16

(a) Use a calculator with mean and standard deviation keys to verify that x̅₁ » 747.5, s₁ » 170.4, x̅₂ » 738.9, and s₂ » 212.1.

(b) Let m1 be the population mean for x₁ and let m₂ be the population mean for x₂. Find a 90% confi­dence interval for m₁ – m₂.

(c) Interpretation Explain what the confi­dence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 90% level of con­fidence, is one region more interesting than the other from a geochemical perspective?

(d) Which distribution (standard normal or Student’s t) did you use? Why?

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