Quant: Hypothesis Testing

When it comes to hypothesis testing, when is the range not the null ± factor * standard error equation but rather Positive Infinity or Negative Infinity. I know that if the Null is > or = , then the maximum range of the interval is infinity. But what if the the hypthesis is < or =, is the minimum range of the interval - infinity? Or is the lower bound range zero instead of negative infinity? Thanks in advance!

One tailed.

umm, could you elaborate slightly please