Question

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Problem 2 (15 marks) Five people have declared their intentions to run for a trustee seat in the next local election. Some political analysts claim that there is no clear preference among the voters. Hence, it is reported that each of the candidate would obtain 20% of the vote on his name. A political poll is conducted during the campaign among 1,020 randomly sampled voters to determine if there is any clear preference among the voters. The responses are shown below. Candidate Responses A 209 B 269 с 229 D 159 E 154 At a significance level a=0.05, can you infer that there is any clear preference among the voters?

Answer 1

HO: THERE IS CLEAR PREFERRENCE AMONG THE VOTERS H1: THERE IS NO CLEAR PREFERRENCE AMONG THE VOTERES FREQUENCY PROBABILITY OBSERVED (o) (P)=1/N EXPECTED E= SUM OF O *P EXPECTED E= SUM OF O*P S.NO color (O-E)^2/E 209 1 A 2B 269 0.20 1020*0.2 0.20 1020*0.2 0.20 1020*0.2 0.201020*0.2 204.0 0.12255 204.01 20.71078 204.0 3.06373 204.0 9.92647 310 229 4D 159 5 E 154 0.20 1020*0.2 204.0 12.25490 TOTAL 1020 1 1020 46.0784 CHI SQUARE TEST STAISTICS =46.078 DF = N-1 = 5-1 =4 P VALUE = 0 CHISQ.DIST.RT(46.078,4) P VALUE SIGNIFICANCE VALUE = 0.05 REJECT HO. THERE IS SUFFICIENT EVIDENCE TO SUPPORT THE CLAIM THAT THERE IS ANY CLEAR PREFERRENCE AMONG THE VOTERES