Please see the setting and reference in Problem 11. Independent random samples from two regions (not those cited in Problem 11) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.

Region I: x₁; n₁ = 15

Region I: x₂; n₂ = 14

(a) Use a calculator with mean and standard deviation keys to verify that x̅₁ » 1387.3, s₁ » 498.3, x̅₂ » 1039.3, and s₂ » 346.7.

(b) Let m₁ be the population mean for x₁ and let m₂ be the population mean for x₂. Find an 80% 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 80% 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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