$H_0 : p=0.5$
$H_1 : p > 0.5 $
where p is the probability of heads from a coin flip.
Let $W_1$ be the number of heads from 10 coin flips and and $W_2$ be the number of heads from 1000 coin flips.
Accept $H_0$ if $W_1 \leq c_1 $ and $W_2 \leq c_2$, otherwise accept $H_1$. Determine the value of $c_1$ and $c_2$, or in other words the number of heads, using a level 0.05 test so that we may accept $H_0$.
I know that coin flips follow a binomial distribution, however I am not sure how to determine the two values using that. So far I've only solved problems with normal distributed random events. I am aware of CLT but is n=10 large enough to use it? For n=1000 it seems more reasonable. So do I have to use the fact that they are binomial distributed or is there some formula or trick that I am unaware of? Any help is appreciated!