I am currently working towards the Royal Statistical Society's Higher Diploma and have run across a strange result in one of their sample papers that I can't work out - wonder if anyone can help me.
In Q3 of this paper you are asked to work out the optimal (Neyman) allocation for strata sizes in a sample.
According to everything I've seen, the formula is:
nh = n * ( Nh * Sh ) / [ Σ ( Ni * Si ) ]
However, in the sample solution the standard deviation seems to be calculated as √(nhph(1 – ph)) - in other words, the nh in the numerator rather than the denominator as is usual in the standard deviation formula for a proportion.
I'm sure I'm being dense and missing something obvious, but I have looked and can't seem to find an answer. Can anyone help me? Thanks so much in advance.