Sample size for variable with many categories in statistical model

I have produced a PWE statistical model with various variables in. We can measure the ‘acceptable sample size’ of a population so to know how many we need to survey- so it might be that we can check the accuracy of our results this way..

If we have 24526 people in a population and of those we had 662 matching on ‘Sunday paper’ (a person can read more than one paper).

At first glance this is quite a low proportion, yet, according to this sample size calculator, if we input a 24526 population, accept a 95% confidence level, and a confidence interval of 5% then we’d only need a sample of 379 people to be 95% confident in the result. 662 would be considered a healthy enough number in this case.

I would like to know whether there is a way I can measure the acceptable sample size which takes into account the different paper categories of the variable. Is there is any skew at all in those records that tend to ‘match.’ i.e. do those 662 tend to be from any particular group/ cohort of society?

Population 24256

The Sunday Times 202
The Weekend 240
The Sunday Telegraph 18
Mail on Sunday 118
The Observer 230
The Independent 133
News of the World 67
Sunday None 45
Total 662