A two sample t-test can indeed tell you things about two population/sample means. Remember though, that these various tests refer to the DISTRIBUTION of values across a spectrum. It is a good idea to review just how the graphs of our Z, T, Chi-squared and F charts look like, but for the moment, we're simply told that we need to use a T-chart to computer this particular Hypothesis Test.
One thing to note before starting, is that we can not PROVE a "null hypothesis". When we are doing a Hyp-Test, we can either reject or fail to reject a "null hypothesis", but we can not "prove" it. Knowing that, we can certainly create a test to determine whether or not our population differences are the result of chance, or whether there is something statistically significant going on to account for their difference.
What is your alternate hypothesis; are the means "not equal", is Mean A greater than Mean B, or is Mean A less than Mean B? All these are valid alt. hypotheses, that need to be defined. In the case here, Mean A is not equal to Mean B would be our alt hypothesis, as you are saying you are told to use a two-tailed test.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.
What is your critical value? Do you know how to calculate this? You can not just grab an arbitrary p-value (well I suppose you can, but they probably don't want you to do this). You are perhaps referring to a SIGNIFICANCE LEVEL of 0.05. And that's fine. However our critical value is going to determine what our P-value is.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.
Now, if the P-Value you manage to calculate is greater than the significance level of 0.05, then we fail to reject the null hypothesis (that our results are simply a matter a chance). If your P-Value is LESS than 0.05, then we can reject our null hypothesis, and say that there is evidence that. . ."lah blah blah" (whatever you set out to test).
Hopefully this isn't TOO cumbersome and you get something of value here. Let me know if you have any questions.