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†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.
Region I: x1; n1 = 12
Region II: x2; n2 = 16
(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to one decimal place.)
(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find an 85% confidence interval for μ1 − μ2.
From the given information,
As given that population is normally distributed for both regions.
Thus, required descriptive statistics can be calculated as;
Region 1) and region 2) with required descriptive statistics are as follows:
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