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 = 12 540 810 790 790 340 800 890 860 820 640 970 720 Region II: x2; n2 = 16 750 870 700 810 965 350 895 850 635 955 710 890 520 650 280 993 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to one decimal place.) x1 = ppm s1 = ppm x2 = ppm s2 = ppm (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.

Question

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
540
810
790
790
340
800
890
860
820
640
970
720
Region II: x2; n2 = 16
750
870
700
810
965
350
895
850
635
955
710
890
520
650
280
993
(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to one decimal place.)
x1
=

ppm
s1
=

ppm
x2
=

ppm
s2
=

ppm

(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.

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