For hypothesis testing you set up two hypotheses. One, the null hypothesis, and a second, the alternative. They should be complementary: That is, if you do not accept one you must accept the other. So x<0 and x>=0 are complementary hypotheses; if x<0 then it isn't x>=0, and vice-versa.
Then generally you test how plausible the null hypothesis is, given your observed data. If the chance of seeing your observed data is very low, you 'reject' the null hypothesis and accept the alternative as being more likely.