That’ll teach me to post without thinking! Yes, you’re right that np(1−p) is the better way to deal with variance here. (Or honestly, the (1−1n)n method from the above comment is the slickest way.)
I had been thinking of a similar kind of situation, where you have a fixed p and varying sample sizes n. Then, the smaller n gives more extreme outcomes than larger n. Of course, this isn’t applicable here.
That’ll teach me to post without thinking! Yes, you’re right that np(1−p) is the better way to deal with variance here. (Or honestly, the (1−1n)n method from the above comment is the slickest way.)
I had been thinking of a similar kind of situation, where you have a fixed p and varying sample sizes n. Then, the smaller n gives more extreme outcomes than larger n. Of course, this isn’t applicable here.