Statistics: (Please show stepts)

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 = 12540810790790340800890860820640970720

Region II: x₂; n₂ = 16750870700810965350895850635955710890520650280993

x₁=   ppm

s₁=   ppm

x₂=   ppm

s₂=   ppm

Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂.

Find a 99% confidence interval for μ₁ - μ₂. (Round your answers to one decimal place.)

lower limit ppm

upper limit ppm

Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is one region more interesting than the other from a geochemical perspective?

We can not make any conclusions using this confidence interval.

Because the interval contains only negative numbers, we can say that region II is more interesting than region I.

Because the interval contains only positive numbers, we can say that region I is more interesting than region II.

Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.

Which distribution (standard normal or Student's t) did you use? Why?Student's t was used because σ₁ and σ₂ are known.

Standard normal was used because σ₁ and σ₂ are known.

Student's t was used because σ₁ and σ₂ are unknown.

Standard normal was used because σ₁ and σ₂ are unknown.