Power test - which one is suitable for me

#1
I have a group of 200 female individuals that are either infected or uninfected.
The infected proportion is known at generation (G) 0 when I mixed infected and uninfected females at 10% (therefore 20 infected, 180 uninfected).
This infection frequency is expected to increase in each generation.
I will test for the infection in each generation after they produce offspring to determine how many are infected.

My first question is, for G0, how many individuals out of 200 do I need to test (it is not practical for me to test all of them) in order to achieve 1-B of 0.8 that the infection frequency is 10% (even though I know that it's 10%)?
My second question is, in subsequent generations as the infection frequency increases (or decreases) how many individuals do I need to test in order to be confident I'm obtaining the true infection frequency with the same power?

I've tried using pwr.p.test in R but the pwr package won't install.
I think this is a power test of a binomial distribution but I'm not sure of effect size (cohen's h I think).

Any help would be greatly appreciated.
Jason
 

Dason

Ambassador to the humans
#2
You can't really test that it exactly is 10%. You can test that it is different from 10% though. You can create confidence intervals that have a certain width. But you can't really ever say that "my test says that the rate is 10%"

With that said why wouldn't pwr install?