1. Help interpreting Goodness of Fit tests please

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.

2. 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.

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