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.
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.
From the given information,
As given that population is normally distributed for both regions.
a)
Thus, required descriptive statistics can be calculated as;
Region 1) and region 2) with required descriptive statistics are as follows:
Image Transcriptionclose
(data - mean) data data-mean 540 -207.5 43056.25 810 62.5 3906.25 790 42.5 1806.25 42,5 790 1806.25 340 -407.5 166056.25 800 52.5 2756.25 20306.25 890 142.5 12656.25 860 112.5 820 72.5 5256.25 -107.5 640 11556.25 970 222.5 49506.25 720 -27.5 756.25
Image Transcriptionclose
Σ п 540 810 .+ +720 12 = 747.5 12 (x-F) Σ(-3) n-1 319425 12-1 170.4
Similarly,
For reg...
Image Transcriptionclose
ΣΣ 750+870+.... +993 16 738.9 1 Σα-3) n-1 675090.9375 16-1 =212.1
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