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?

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?