Excel Statistics

I would say this is more of a statistics question than an Excel question. I'm not sure if we have anyone on this board who is enough of a statistician to give you a thorough answer. I also expect that the answer could be found in any intro to stats text or online tutorial.

My intro to stats text has this to say about the p-value: "the level of significance [p-value] represents the probability of observing a sample outcome more contradictory to H0 than the observed sample result if, in fact, H0 is true. The smaller the value of this probability, the heavier is the weight of the sample evidence for rejecting H0." -- Ott and Mendenhall Understanding Statistics 4th edition.

Wikipedia has this article: http://en.wikipedia.org/wiki/Statistical_significance

ok, so to start with your problem see what we have: some data and α=0.05. Then you use statistical tables to check the value - for α=0.05 is 1.96.

And now, you have t-test (two-tailed) results given for the Excel: a t-test result of 0.65 and a p-value of 0.5

It's just enought to see that the calculated p-value /here 0.5/ is > than α=0.05. So we do not reject the null hypothesis. It also means that the output is not considered statistically significant
When you use any statistical package you will be provied not only with a t-test result but with other information.

We can also check: lf t Stat < -t Critical two-tail or t Stat > t Critical two-tail, then we reject the null hypothesis. In this case we have:

is FALSE in this case: 0.65 < -1.96 or 0.65 > 1.96 - if the condition is true we reject the null hypothesis /means/ a p-value is found to be less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected
if a p-value < 0.05 it indicates that the observed result would be highly unlikely under the null hypothesis

TRUE: -1.96 < 0.65 < 1.96. - we do not reject the null hypothesis