Inorganic phosphorous is a naturally occurring element in all plants and animals

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. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions

(a) Use a calculator with mean and standard deviation keys to verify that x1, s1, x2, and s2. (Round your answers to one decimal place.)

(b) Let 1 be the population mean for x1 and let 2 be the population mean for x2. Find an 80% confidence interval for 1 2. (Round your answers to one decimal place.)

Region I: x1; n1 = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020

Explanation / Answer

Instructions for TI83/84 calculator:

First enter x1 data in L1 and x2 data in L2.

Press 2nd and then Mode to quit from editor.

Press STAT->CALC and select 2-Var Stats.

XList: L1

YList: L2

FreqList: (leave blank)

Press calculate.

(a) Use a calculator with mean and standard deviation keys to verify that x1, s1, x2, and s2. (Round your answers to one decimal place.)

(b) Let 1 be the population mean for x1 and let 2 be the population mean for x2. Find an 80% confidence interval for 1 2. (Round your answers to one decimal place.)

Press STAT->TESTS->2-SampTInt...

Inpt: Data

List1: L1

List2: L2

Freq1: 1

Freq2: 1

C-level: 0.80

Pooled: No

Press Calculate. The output gives:

x1 = 1387.3 ppm s1 = 498.3 ppm x2 = 1039.3 ppm s2 = 346.7 ppm

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