Inorganic phosphorous is a naturally occurring element in al

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.

(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 ₁ be the population mean for x₁ and let ₂ be the population mean for x₂. Find a 99% confidence interval for _{1 2}. (Round your answers to one decimal place.)

Solution

a)
Mean(x1)=747.5
Standard deviation( sd1 )=170.407
Sample Size(n1)=12
Mean(x2)=738.938
Standard deviation( sd2 )=212.146
Sample Size(n1)=16CI
b)
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval

CI = [ ( 747.5-738.938) ±t a/2 * Sqrt( 29038.545649/12+45005.925316/16)]
= [ (8.56) ± t a/2 * Sqrt( 5232.75) ]
= [ (8.56) ± 3.106 * Sqrt( 5232.75) ]
= [-216.12 , 233.24] ~ [ -216.1, 233.2 ]