One-sample t-tests and bonferroni


I'm wondering about whether I need to use the Bonferroni on my data. I need to run 9 one-sample t-tests to calculate whether observed data (in the form of a proportion) for each subject differs from a hypothesized value of 0.5. So I'm guessing I need to adjust the p-value to prevent inflating the risk of an error, or is this not the case because I'm not doing multiple analyses on the same set of data?

So, excuse my ignorance but is the bonferroni procedure as simple as just running the t-tests as normal and then considering the outcome as significant only if p < (0.05/9)? So, a test that would normally come out at, say p = 0.03 still comes out as p = 0.03 but I consider it insignificant because my new value is 0.006? Or does it require altering the procedure too to take this into account? It seems somehow too simple.. It also seems overly stringent for this type of data - is there a way of running multiple sets of data against a hypothesised value in a single test (rather than against each other)?

I hope that someone can help. Thanks!