A Simple Random Sample Without Replacement (SRSWOR) survey is conducted that included too many women and not enough men in the sample
In the resulting weighting, each female is given a weight of $1$ and each male respondent is given a weight of $1.5$.
This sample included $600$ women and $380$ men, of whom $400$ women and $100$ men respond Yes to a particular question of interest.
Give an estimate and standard error for the proportion of adults who would answer Yes to this question?
I understand how to do this regularly it is just the weightings have thrown me off and I am becoming confused.
Initially I would have thought the estimate would be:
$\dfrac{500}{980} = 0.51$
However with the weightings I am not sure if this is still the correct answer.
With the standard error I would have again found the sample error(s) of each sex but again what do I do with the weightings?
Any help would be much appreciated
Thank you