Question

Problem 1 An imaginary study is concerned about the possible radioactive contamination caused by the recent nuclear plant accident in Japan. The average radioactive contamination level (denoted by Y) is measured in 10 cities around Japan after the nuclear accident. Their distances to the nuclear accident (denoted by X) site are also provided. The historical radioactive contamination level measured before the nuclear accident (denoted by Z) is also provided. Y X Z Individual 45,45,55,55,56, 10,9,8,8,7, 45,44,54,53,53, data points: 62,65,65,75,78 5,4,1,2, 2 5 8,61,60,70,70 Sample mean 60.1 5.6 56.8 Sample SD 11.15 Sample Size 10 10 10 (a) Is the correlation between Y and X significantly different from zero? Perform one formal statistical test to justify your claim. (b) Is the correlation between Y and Z significantly bigger than 0.8? Perform one formal statistical test to justify your claim. (c) What nonparametric test can be used to compare Y with Z in order to check whether the contaminant level has increased after the nuclear accident? Does this data set support the use of your chosen nonparametric test? (d) Did the nuclear plant accident significantly increase the radioactive contamination level of its nearby cities?

Answer 1

lleder Y Aug xadiogetive contamination lend. X distance to the nuclear accedant 2 -> adioactive contamination linal measurew before the nuclear accident. - 6.6 so & 56.8. y = 601 Sy = 11:15 = 5.6. sx - 3024 S2 = 8.93. Coro 3 n = 10 na 10 rm 210 a Samble covel ation Co-eff reilut befw Y fx is- de a {(xi-x) (v: -7). Now, un [ Rig - mag] (3068 – 1045-6*60"] = - 33.067 x= (-33-067)/(15*3'24) --0-915 Ho: e=0 us. Hilto, to statistie is- to = rin.2 WI-2 40.915 vs. di- (0.915) ? : -6.426.

Under Her ta tn-2. . tioosis = 2.306 - 6426 < -2.306. ons is significant Corren b/w Yex b. Heyz diffen significantly from o. 3 (4.5) (2;-) Sp.st 2 ) 2 + 2 g - 2( 5 ( . 35029 - 10x 60.1856.8]. 99013 Stayz - 99.13 15*8.93 -0.99 56. o' t.. 0.9956 1 20:30-OSTS 0.9956 1.025,8 = 2.306. . 30.0515) 2-306 & is ensignificant Corral 6/0 Y 8 z differe significantly fono

that To compan Yez. parce Sample Wileeson. accident signed reant lest is used 2 die (-2) squa sent (ignores) Signs Rank [ignores) d). T Sny livet - 1.5 15 55 . . - . Assum . 5.5 . M2 - 65 &. 75 Test & 8.5 & o 78. 9 Whe Hos To S 0:0 vs. when I is Tt Sum of H: 0 0 . the median of distrito positive seanks : 45 of differences Undra % TEO. To mir (T+, T-) = 0. & d=0.01. To = 5 Sunce there is T < To nee sufficient evidence may corelude to preject the mell lupothes

that there ls some effect of nuclear accident in favour of the alterenative at 10% level. blant hypothesis To ten vihether if the nuclear plant are ly increase the radioactive contamination liver of ils nearby cities, the hypothesis of interese is Hos sy = fyz vs. Hi! My >Mz. Assumption", Y Z Z are j thy normally distribected. My = radioactive arg. 4 contamination 4 accident level. after before Test statistie – to in Sa. where, ue= y 2 . Under 40. tn tnar ū = ý -z = 60.1 56.8= 3.3 Varelule Su = 2.406 - E NTO 13:3 2.40.6 tag= 2.82 le hypothes

i. It is significant at 10% level of significance. en he should say that there is significant increase abr the radioactive contamination lend of the nearley cities due to the nuclear plant accident