# Sample sizes: stratified random vs simple random sampling

In general, how does the total sample size for stratified random sampling compare with sample size for simple random sampling?

The variable involved is binary: yes-no. The population parameter to estimate is the proportion of Yes. (For example, say there are 800 cases in 25 cities. I could form 25 strata or group the cities into 5 geographic areas to form 5 strata. (The parameter of interest is the proportion of Yes, nationwide.)

I am thinking of using strata to avoid my random sample from being strange or lopsided.