1. Environmentalists would like to stop coal-burning companies from emitting mercury, because they believe it is contaminating the fish. Mercury is now at dangerous levels in many river fish. Coal-burning companies claim that they are not to blame -- the fish are getting mercury poisoning from some other source. To settle the matter, some data was collected about the mercury levels in various rivers and their proximity to coal-burning plants: Proximity to coal-burning plant (in miles) Mercury level 180 60 150 65 20 96 670 41 For ease of calculation, here are some pre-computed values: sum(x) = 1020 sum(y) = 262 sum(x*y) = 49940 sum(x*x) = 504200 sum(y*y) = 18722 mean(x) = 255 mean(y) = 65.5 a) Find the correlation between proximity and mercury level. Solution: r = (4*49940 – 1020*262) / (sqrt( 4*504200 –10202) sqrt(4*18722 – 2622) ) = -0.86 b) Test whether there is significant evidence that proximity and mercury level are related at the .05 level. Find b’: b’ = (4*49940 – 1020*262) / ( 4*504200 –10202) = -.069 Find �2’ a’ = y_bar – b’*x_bar = 83.095 ssyy’ = sum((y_i – y’_i)2) = (60 – 70.675)2 + (65-72.745)2 + (96 – 81.715)2 + (41 – 36.865)2 = 395.1 �2’ = ssyy’/(n-2) = 58277/2 = 197.55 Test whether b = 0: ssxx = sum((x_i – x_bar)2) = 244100t-obt = .069 − 2.43 = − . 197.55 244100 At df=2, t_crit = 4.303, thus there is not significant enough evidence to conclude that the two are
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