you just gave me some warm fuzzies my friend! haha a z-test and t-test are just statistical hypothesis tests. A p-value is very important, it is the probability that there is more condemning evidence against the null hypothesis given the current sample size. The power of the test is just the complement of the p-value (1- pvalue = power) the power is just the probability that we will reject the null hypothesis when the null hypothesis is false. (A null hypothesis is what we assume to be true).