I am currently studying for an midterm, and am running into a roadblock with some of the concepts concerning hypothesis testing applied to means with two related samples. I am noticing in all of the examples in the textbook that the null hypothesis (mu) is always Ho = 0. Why is it that for this particular type of hypothesis testing, mu is zero when in nearly all of the other kinds of hypothesis tests (hypothesis testing with independent samples, hypothesis testing with a single observation) the null can be a variety of numbers? With related samples, is the null ALWAYS zero or is this just due to limited examples in the book? Perhaps this seems like a very obvious question, but I did poorly on my first exam and I think this is because I did all of the homework questions but didn't fully understand the concepts behind the answers I was getting.

I am also running into a bit of confusion knowing exactly what tests to apply to certain questions. I am never confident knowing whether to use a t-test or a z-test (the same applies to t and z confidence intervals) or whether to solve for independent samples or paired samples. Any words of advice or things in particular I should remember to help me out would be greatly appreciated, I know all of this probably seems very straightforward but I have to put my dignity aside for a moment and go ahead and display my ignorance to the world.

Thanks much!