Suppose three political candidates are running for the same elective position. P

Question

Suppose three political candidates are running for the same elective position. Prior to the election, we conduct a survey to determine the voting preferences of a random sample of 150 eligible voters. The qualitative variable of interest is preferred candidate, which has three possible outcomes: candidate 1, candidate 2, and candidate 3. Suppose the number of voters preferring each candidate is tabulated and the resulting count data appear in the below table. Use a proper statistical test to decide whether the voters, in total, have a preference for any one of the candidates.

Explanation / Answer

if theyr are uniform then probabilty for each candidate to get votes should equal to 1/3

here applying chi square goodness of fit on above:

for above chi stat 6.52 ; for 2 degrees of freedom p value =0.0384

as p value is less then 0.05 level we reject that voters choice is independent of candidate and conclude that preferencve exist

observed Expected Chi square candidate P O E=total*p =(O-E)^2/E 1 1/3 61 50 2.42 2 1/3 53 50 0.18 3 1/3 36 50 3.92 150 150 6.52

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