The following problem is from a. current\") research project in groundwater modeling. This research is part of an ongoing effort to aist the Ivnnesota Department of Health11 in the characterization of wellhead protection areas. Wellhead Protection is a way to prevent drinking water mn becoming guilluted by managing potential sources of contamination in the area which supplies water to a public well. Much can be done to prevent pollution, such as the wise use of land and chemicals. Public health is protected and arpense of treating polluted water or drilling new wells is avoided though wellhead protection efor'ts. httpe : Hm. health. state .mn. usfcamunitiesfenviranmntfwaterl as]?! index . hm The particular problem at hand is the estimation of the hydraulic conductivity\" of an inhclnclogeneitbrm in the aquifer using eld measurements. Consider an aquifer with the basic properties given in Table 4. We consider a set of 25 head\" measurements taken at 25 known locations {Xingu} 11': 1: 2+U'T25 (6) and we denote the associated head measurements Macmyn} = {la n a 1,2. . . . .25 (7) The data is given in Table 5. The theory of groundwater mechanics1'\"I tolls us that the 1.rarious aquifer properties and measured heads should be related by {3) for the particular setting at hand\". kc _ k 1': for n. = i, 2, . . . .25. Using algebra, we reorganize (8) to read khn + Qua!\" _ C kg _ k x\\fg Y\" = PH 5:, mm] are the dependent variables, a X\" = [-55%] are the independent variables, a Q45) is the intercept, and o (iit) is the tted slope, from which we compute the inferred kc. Equation [:9] becomes 71-; = {I + an (1D) where the two unknowns are _ C _lcck _on? \"'1 \"kt-+1: l\") a. Using the data in Table: 4 and 5, estimate the value of B in (10) using simple linear (least squares) ragteESion. 61'. b. Compute an approximate 95% condence interval for the estimated value of B'- C. Using your estimated value for , estimate a value for 12;. Yes, this will require a small bit of algebra.r d. Compute an approximate 95% condence interval for the estimated value of it.\" \f