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 regiond. 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.
(b) Let ?1 be the population mean for x1 and let ?2 be the population mean for x2. Find a 95% confidence interval for 1 and 2.
(c) 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 95% level of confidence, is one region more interesting than the other from a geochemical perspective?
A. Because the interval contains only negative numbers, we can say that region II is more interesting than region I.
B. We can not make any conclusions using this confidence interval.
C. Because the interval contains only positive numbers, we can say that region I is more interesting than region II.
D. Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.
(d) Which distribution (standard normal or Student's t) did you use? Why?