I am really struggling with the following question. I'll describe the situation.
If we do x coin tosses, then the chance that we have more heads than tails (H>T) is described by equation 1 below.
If we do x coin tosses, then the chance that we have an equal number of heads and tails (H=T) is described by equation 2 below.
Finally, if we do x coin tosses, then the chance that we have more tails than heads (H<T) is the same as for equation 1; shown in equation 3 below.
Now I have a situation where this entire situation is repeated y times, but with different x. For example, let's say y=7 and I know x for each y. For example, x∈{1,4,4,5,10,14,17}. For this example, if I see, respectively H>T, H=T, H>T, H>T, H>T, H>T, H<T, then how can I statistically test the hypothesis that in this situation H>T is more likely to occur than expected by chance?
I am hoping there might be a way to generalise this, because I have multiple different y's, so I am hoping for a general answer that I can apply to all my different y's.