First off, I am new to this forum and would like to take this chance to say hi to everyone.

I am currently working on a statistics project, and I ran into a question concerning how two-tailed probability should be calculated under a Monte Carlo sampling situation.

So, I have this ratio (say 0.9) that I computed from a sample of data. I wanted to know if this ratio is different from those of samples drawn from a population whose ratio value is one. To do this, I created a large experimental data set that has a ratio of one. I then sample from this data set with a sample size equal to that of the sample in question over 10000 times with replacement.

Out of the 10000 iterations, 400 cases have ratios equal to or lower than 0.9. So the empirical probability for a sample with a ratio of 0.9 to be drawn from a population that has a ratio of one is p=400/10000=.04

However, here comes my question. This p (.04) is one-tailed at the moment. If I want to get a two-tailed p for this, do I have to account for the cases that are on the other side of the distribution? If so, do I just multiply this p by 2, or actually look for cases that are of the same distance to the mean as 0.9? I have talked to a researcher who said that since I got the empirical p, I don't need to worry about the other side of the distribution and just use a critical value of .025. Is this correct?

Thanks for the help!