Extracted text: 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. region i: x,; n, = 15 857 1,553 1,230 875 1,080 2,330 1,850 1,860 2,340 1,080 910 1,130 1,450 1,260 1,010 region ii: x2; n2 = 14 538 810 790 1,230 1,770 960 1,650 860 890 640 1,180 1,160 1,050 1,020 n use salt (a) use a calculator with mean and standard deviation keys to verify that x,, s,, x2, and s,. (round your answers to four decimal places.) x, = ppm s, = ppm x2 ppm s2 ppm %3d (b) let u, be the population mean for x, and let µ, be the population mean for x,. find an 80% confidence interval for h1 - h2. (round your answers to one decimal place.) lower limit ppm upper limit ppm (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 80% level of confidence, is one region more interesting than the other from a geochemical perspective? o because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other. o because the interval contains only positive numbers, we can say that region i is more interesting than region ii. o because the interval contains only negative numbers, we can say that region ii is more interesting than region i. o we can not make any conclusions using this confidence interval. (d) which distribution (standard normal or student's t) did you use? why? o student's t was used because o, and o, are unknown. o standard normal was used because o, and 0, are known. o standard normal was used because o, and o, are unknown. o student'st was used because o, and o, are known. 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.="" region="" i:="" x,;="" n,="15" 857="" 1,553="" 1,230="" 875="" 1,080="" 2,330="" 1,850="" 1,860="" 2,340="" 1,080="" 910="" 1,130="" 1,450="" 1,260="" 1,010="" region="" ii:="" x2;="" n2="14" 538="" 810="" 790="" 1,230="" 1,770="" 960="" 1,650="" 860="" 890="" 640="" 1,180="" 1,160="" 1,050="" 1,020="" n="" use="" salt="" (a)="" use="" a="" calculator="" with="" mean="" and="" standard="" deviation="" keys="" to="" verify="" that="" x,,="" s,,="" x2,="" and="" s,.="" (round="" your="" answers="" to="" four="" decimal="" places.)="" x,="ppm" s,="ppm" x2="" ppm="" s2="" ppm="" %3d="" (b)="" let="" u,="" be="" the="" population="" mean="" for="" x,="" and="" let="" µ,="" be="" the="" population="" mean="" for="" x,.="" find="" an="" 80%="" confidence="" interval="" for="" h1="" -="" h2.="" (round="" your="" answers="" to="" one="" decimal="" place.)="" lower="" limit="" ppm="" upper="" limit="" ppm="" (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="" 80%="" level="" of="" confidence,="" is="" one="" region="" more="" interesting="" than="" the="" other="" from="" a="" geochemical="" perspective?="" o="" because="" the="" interval="" contains="" both="" positive="" and="" negative="" numbers,="" we="" can="" not="" say="" that="" one="" region="" is="" more="" interesting="" than="" the="" other.="" o="" because="" the="" interval="" contains="" only="" positive="" numbers,="" we="" can="" say="" that="" region="" i="" is="" more="" interesting="" than="" region="" ii.="" o="" because="" the="" interval="" contains="" only="" negative="" numbers,="" we="" can="" say="" that="" region="" ii="" is="" more="" interesting="" than="" region="" i.="" o="" we="" can="" not="" make="" any="" conclusions="" using="" this="" confidence="" interval.="" (d)="" which="" distribution="" (standard="" normal="" or="" student's="" t)="" did="" you="" use?="" why?="" o="" student's="" t="" was="" used="" because="" o,="" and="" o,="" are="" unknown.="" o="" standard="" normal="" was="" used="" because="" o,="" and="" 0,="" are="" known.="" o="" standard="" normal="" was="" used="" because="" o,="" and="" o,="" are="" unknown.="" o="" student'st="" was="" used="" because="" o,="" and="" o,="" are="">