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I'm trying to analyze the results of a survey question. The question is multiple choice (but each respondent can only select one answer) and I want to calculate 95% confidence intervals for their responses.

A      122
B       55
C       16
D       14
E       13
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Total  220

If I'm using R, can I treat each choice as a binomial (122 out of 220 chose A, 98 did not choose A) and use binconf() to compute the interval or is there a better method for categorical data?

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I think you should use multinom instead. A multinomial distribution is a generalization of the binomial distribution for independent trials.

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