I want to do statistical analysis to compare the results of the different specimen sizes (which I am comparing) with each other. Seeing as I have at least 12 specimens for each specimen size, I thought it was possible to use the data sets to compare the means and identify the differences between these values. I then thought that I could do this using a two sample $t$ test to try and determine the difference in the population means.
My question is, is this possible? How can I justify the data is Normally distributed to allow this
EDIT: As well as this, is it correct wording to say:
I used a hypothesis test to test the differences in the two sample populations and tested the validity of the claim null hypothesis versus the alternate hypothesis. I determined a level of significance ($\alpha$ value) tested the null hypothesis against a probability value ($p$ value). If my $p$ value > $\alpha$ value, then I can accept my null hypothesis. Once I had accepted (or declined) the null for each data set, I can then carry out my $t$ test to compare the independent sample means.
Is $p$ value correct there, or should it be $t$ value?