Question

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Problem 7 An opinion poll of registered voters is performed to estimate the support for an Important Ballot Initiative. Each person polled can indicate they support the intiative (S) or do not support it (D) A lf N people are polled, write down a probability distribution function that should describe the chances of finding that n respondents support the initiative, if any given voter has unknown chance p of supporting the initiative. B The poll takes place. It is found that 88 people support and 95 people do not support, what is p as defined in Part A? what is the margin of error (in %) for the poll?

Answer 1

A. The no of voters supporting the initiative can be modelled using binomial distribution, since there are N independent people polled, where probability of each person supporting the initiative is p, independent of the others . So required probability of n people supporting the initiative is,

P(N=n) : NCn*p^n*(1-p)^N-n

This is a binomial distribution with parameters N, p

B. p as defined above would be 7/95 from this data ie 0.074

Margin of error = z score confidence level*√p(1-p)/n

So it will be, z score*0.027

If we take 95% confidence level as taken generally, the margin of error will be, 1.96*0.027 = 0.053