In Professor Boneh's online Cryptography course at Coursera, I am a little puzzled by his definition of a statistical test where he writes:
A(x) = iff |#0(x) - #1(x)| <= 10.√n
Now, if – as an example – we were to perform this test on a string of $100$ bits, then $10$ multiplied by the square root of $100$ is… $100$. But if we had a hundred $0$s in this string and no $1$s then A would output $1$, i.e. would judge the string as random.
Am I perhaps misunderstanding something?