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Question

in a election, candidate A received 10% of the vote, candidate B received 64%, and candidate C received 26%. For a random group of 30 people, find the probability that 8 voted A, 17 voted B, and 5 voted C.

Answer 1

First recognize that this problem is presenting you with categorical data. So a chi-square analysis is appropriate here.

 

Next, recognize that the problem is presenting you with a distribution, i.e. A-10%, B-64%, and C-26%. The problem is asking you to compare the sample distribution to the known distribution. Thus, use a chi-square goodness of fit test here.

 

Using a calculator, I get a p-value of 0.0083. This means that if I truly sampled from the population and the distributions are the same, there would only be a 0.83% probability of obtaining the observed values. Thus one might conclude some type of sampling error.