Just for the fun of it, we can carry out one additional test and ask a rather specific question: If both proportions are 0.388 in the population and the other three are identical to their values in the sample, what is the probability of observing a difference of at least 4.4 points in favour of right-wingers?

The idea is to sample repeatedly from a multinomial with known probabilities. This could be done more elegantly by defining a program and using Stata’s simulate command, but if your machine has enough memory, it is just as easy and possibly faster to use two loops to generate/analyse the required number of variables (one per simulation) and to fill them all in one go with three lines of mata code. Depending on the number of trials, you may have to adjust maxvars

local trials = 10000
foreach v of newlist s1-s`trials' {
qui gen `v' = .
}
mata:
probs =(.388,.388,.056,.038,.13)
st_view(X.,.,"s1-s`trials'",)
X[.,.] = rdiscrete(1043,`trials',probs)
end
local excess = 0
forvalues sample = 1/`trials' {
qui tab s`sample' if s`sample' == 1
local rw = r(N)
qui tab s`sample' if s`sample' == 2
local isl = r(N)
if (`rw' / 1043 * 100) - (`isl' / 1043 * 100) >=4.4 local excess = `excess' +1
}
display "Difference >=4.4 in `excess' of `trials' samples"

Seems the chance of a 4.4 point difference is between 5 and 6 per cent. This probability is somewhat smaller than the one from the multinomial model because the null hypothesis is more specific, but still not statistically significant. And the Zeit does not even have a proper random sample, so there is no scientific evidence for the claim that Germans are more afraid of right-wing extremists than of Islamists, what ever that would have been worth. Bummer.