Help interpreting Goodness of Fit tests please

[somnum]

Hi. I'm trying to figure out if I am able to run the t-test on my data, or if I am forced to run non-parametric tests.

If I run the chi-squared, or the kolomogrov-smirnov, or the anderson-darling etc, how do I interpet the data that spss is giving me. If I accept H0, does that mean that my data fit the distribution of the test? So if I accept H0, does that mean that my data have a shape consistent with the chi-squared for example? Do I have to run every test until I get an acceptance of H0, and then I am able to tell if my data are parametric or not?

Thank you.

[somnum]

Scratch that, I've done some tests on it, and apparently it fits an exponential curve pretty well (doing p-p or q-q plots). Also, if I natural log transform the data, it fits very well. However, as you might expect, it fits a normal distribution or t distribution terribly. My question is this, since the natural log makes it look pretty well, am I able to natural log transform it and then run the t-test on it? Because if I run non parametric tests on the data, they come back as insignificant, whereas a t-test shows it as being significant. I want it to be significant, but not at the expense of validity. I realize I lose power with non-parametric tests, so hopefully I would be falsely rejecting Ha.
Finally, I am running the t-test on a group that comes in 10's of percents - 0 (many) to 100 (few) -, and affects a certain dependent variable (lifespan). In SPSS, I select a cutoff point of 25&#37;, that yields significant results...do I need to run a goodness of fit on the <=25% as well as the >25%, or am I able to run a goodness of fit on the whole thing?
Am I correct in assuming I don't need to run a goodness of fit on the dependent variable because it is irrelevant for the comparison of means test?

Pictured are examples of what I'm talking about.