with the alternative hypothesis the reasearcher is predicting

A statistical hypothesis is anything that can be tested against observations. So the hypothesis can be that you can remember two numbers.

A statistical hypothesis test will usually be performed by inductively comparing results of experiments or observations. The number or amount of comparisons will generally dictate the statistical test to use. The researcher is basically making a statement and assuming that it is either correct (the hypothesis - H1) or assuming that it is incorrect (the null hypothesis - H0) and testing that assumption within a predetermined significance level - the alpha.

I think you are asking: What is hypothesis testing in the field of statistics. See: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

It is the hypothesis that is presumed true until statistical evidence in the form of a hypothesis test proves it is not true.