Question

Following is a random sample of 15 measurements from high-flow rivers and 13 from low-flow rivers of a total algae concentration. High Low 23.3 18.4 23.8 59.6 33.6 36.6 41.8 47.3 56.0 34.1 78.8 33.3 17.8 55 31.0 43.1 23.4 26.0 49.5 41.8 65.0 38.7 75.8 11.8 43.9 16.4 48.5 56.4 Is there evidence to suggest that the standard deviations of the aglae concentration in the two types of rivers differ? Use a = 0.02. Round your answers to two decimal places (e.g. 98.76). Reject the null hypothesis if fo or fo > What is the test statistic? Round your answer to two decimal places (e.g. 98.76). fo

Answer 1

F = 82 We have test thate hypothes is that The standard deviation of the aglae concentration in two types of river are differ. i.e. Null Hypothesis. Ho: o, 302 against Alternative hypothesis Ha: 0 to 2 we used E-test to test equality of two variances The value of F-test static ~ Ini-1, M2-1 S22 Here S, = 5₂ = S, =S₂ = Sample variances of agalae concentration in first and second river D.F! Mi-15-1 - 14 n2-113-1 = 12 • Test is 2-tailed we reject to if Fo > Eni-1,02 1,0/2 cor Fo< fri- 1,02-1, 1-2/2 from F-table Fn-1,02-1514,12,0.01 = 3.80 Fr 1-1, M2-1, 1-a = F14, 12,0.99 = 3.66 ie we reject Fo>3.66 or Fo 23.80.

(XI-XI)? (x2-x2) XL 59.6 36.6 34 X2 23.3 18.4 452.41 23.8 431.39 120.34 47.3 7.67 130.640 33.3 1171 69 55 716.63 3.1 184.14 26 448.16 418 24.30 38-7 17.38 11-8 975.31 16.4 0.44 15.44 139.94 462.1 5235.94 668-6 X = = 44.57 + X2= #621 35.54 33.6. 41.8 56.0 78.08 17.8 310 23.4 49.5 65.0 158 43.9 485 564 668.6 293.77 578.88 1-12 138.29 2.07 5.01 378.69 51-15 91.01 39.18 9.98 563.58 366-33 2525.13 5235.94 2 {(x1=7 ) 2 = 373.99 si ni-1 2525.13 3 = 210.41 S2 12 Fo = 12-1 373.99 210.45 1.77 Fo=1.77 since value of to lies is (3.66, 388). we reject the null hypothesis at 21,100 conclusion: we got evidence, support to claim that the std deviation of the aglae concentration in a types of en we