> the president's name will start with a letter in the first half of the alphabet

Sorry, this triggered my fact-checkitis. I opened Wikipedia's list of presidents of the US and ran this in the web developer console:

    Array.from(document.querySelectorAll(
        '#mwgA tr > :nth-child(3) span[data-sort-value]'
    ))
    .map(x => x.getAttribute('data-sort-value')[0])
    .reduce(({total, firstHalf}, c) => ({
        total: total+1, 
        firstHalf: c < 'N' ? firstHalf+1 : firstHalf
    }), {total: 0, firstHalf: 0});

and it responded

    Object { total: 47, firstHalf: 31 }

Then I used Agresti and Coull's method for a 95 % confidence interval around this (add two successes and two failures, compute Wald interval as usual). That gives us

    65 % ± 13 %

In other words, the 95 % confidence interval of the proportion lies in the span from 52 % to 78 %. That is significantly different from the null hypothesis.

I didn't expect it, but we might actually have reason to believe US presidents more often than not do have names starting with letters from the first half of the alphabet.

Edit: But I just realised English letter frequencies have 54 % of the probability mass in the first half of the alphabet, so that's probably a better null hypothesis than the even split. It's also compatible with the actual presidential statistics.