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 Irelands 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 x 1 n 1 12 Region I x 2 n 2 16 (a) Use a calculator with mean and standard deviation keys to verify that x 1 747 5, s 1 170 4, x 2 738 9, and s 2 212 1 (b) Let m1 be the population mean for x 1 and let m 2 be the population mean for x 2 Find a 90 confidence interval for m 1 m 2 (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 Students t) did you use Why 540 810 790 790 340 800 890 860 820 640 970 720 750 870 700 810 965 350 895 850 635 955 710 89 520 650 280 993

Question: Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals

Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit

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?

540 810 790 790 340 800 890 860 820 640 970 720 750 870 700 810 965 350 895 850 635 955 710 89 520 650 280 993

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