Assume the sample size will have to be large, so we can use the normal approximation where we need. Let the sample size be and the proportion who favour the tax be . Then the expected number in the sample will be , and we will estimate this by where is the number in the sample favouring the tax. Then the variance of is and this has a maximum when , so we assume for the purposes of calculating the variance.

Now a 95% inteval for is of width (this is assuming the normal approximation) and we want this to be less than or equal ( that is )

So we put:

and solve for to get the required sample size.

CB