Some background about myself: I have sufficient knowledge in probability but not in statistics.

Suppose I have $n$ i.i.d samples, $\{x_i\}$, sampled from an unknown distribution $X$. I want to conduct a statistical test using this sample to determine if $f(X)$ is "skewed towards positive" or negative value. Specifically, $f(X)$ is said to be "skewed towards positive" if $f(X) > 0$ for more than 50% of the whole population of $X$. What is the appropriate statistic test for this case? Answers with some assumptions on $X$ are also welcome.

I think, I need to first define a null hypothesis that is $f(X)$ is "skewed towards positive". Then, I evaluate $\{f(x_i)\}$ for all samples and decide whether number of observation of positive values surpasses the negative values. Is this a correct statistical test or is there a better test?