writer: of course my study is statistically valid.
Here are the numbers:
The population is 100. I assign a value of 1 to girls and 0 to boys. My null hypothesis is that the underlying population mean is .5
My sample size is 20, randomly chosen. My sample mean is 1.
Thus, the standard deviation of the population as hypothesized is .5 (sqroot of .5*.5).
The standard deviation of sample means is .11
My sample mean was 1, which means it is almost 5 standard deviations off of my hypothesized population mean. So I can certainly reject my null hypothesis.