How do you conduct disproportionate stratified random sampling?
| Home | Office | Total | |
|---|---|---|---|
| Men | 100 | 250 | 350 |
| Women | 120 | 30 | 150 |
| Total | 220 | 280 | 500 |
An overall sampling fraction of 10% has been decided on.
Suppose the company wishes to use a larger sampling fraction of female employees. If they wish to sample 15% of the women in each location category, while still keeping the overall sampling fraction the same at 10%. How many players will be sampled in each category?
Is there a formula which I should be using?
Best Answer
You need just to set up some equations representing the situation.
The overall sampling units are $n = 500 \cdot 10\% = 50$, also
$$n = n_{1} + n_{2} + n_{3} + n_4$$
where each $n_i$ represent the units sampled in a stratum, then $n_3 = 120 \cdot 15\% = 18$ and $n_4 = 30\cdot 15\% = 4.5$ which has to be made an integer either $4$ or $5$, say $5$.
So you can see that $n_1+n_2 = 27$, any combination of integer will be good. I left to you if the numbers with which you obtain the same proportion for each male category if you wish to find them.