How to interpret results from a t-test

Hi,

I have a question regarding how to interpret values from a t-test. If you could help me it would be greatly appreciated.

I have two populations for which I sent a survey out to and got a number of responses back. The survey consisted of a question that had a rating scale of 1 to 5. I worked out the means of both populations so I can compare how they differ. Now I have come to do a t-test. I am reading different things, on what the t-test does, I have read that it will tell me:

- How statistically different two means are

- How likely the results are due to chance

I am doing a 2-tailed independent t-test, and my null hypothesis is that there is no difference in the means of the two populations. I have decided to use a 0.05 p-value threshold.

And this is where I get stuck, if my p-value is greater than 0.05, how do I interpret this, which one of these is correct:

- P-value greater than 0.05, therefore the null hypothesis is accepted and I say that the means are statistically the same.

Or

- P-value greater than 0.05, therefore theses results have occurred by chance

Which one is it? Is it both? If it is both, why are they related?

Thank you

Richard