&NOVpothesis testing for proportionsobjectives : :Z- - test (basically use FortestFor testing goodness of fitonlyFor testing independence of twoP-Plevel of significanceattributespq0.05h2Degree of freedomXfor testing goodness of fit81) see the situation (one failed orforTwo - tailed)Hypothesis testing when 2 sample2) State Ho & H,proportions3) Test Statistics of x2: [c.v]^Z= P, - P2x2=E(0-E)2EP.q.1/2+n,1/2n2where,observed frequencyWhere,E^Expected frequencyPo =n, P, +n2 P24) Find the T.V using X'tablen, + n2level of significance = 0.05q. = 1-Podegree of freedom (---)Hypothesis testing for positively5) Compare T.V & C.VSkewed distribution:T.V > C.VHo is accepted1) Chisquare distribution (x2x2 for testing indepence of twoattributes2) F distribution3) AnnovaTest statistics : [c.v]x2 = E [6-E)2] E1) Chi- square (x2)For Table value :Acceptancelevel of significance 0.05regiondegree of freedom (2-1)(n-1Rejectionregionrno. of rowsRejectionnRegionno. of columnsX2.x x2 X2dh

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