There's something basic I'm not getting here - hope someone can help me out! Say you have hypotheses H0:theta=0 and H1:theta<>0. You calculate the appropriate test statistic under H0 and see if it is in the critical region for the appropriate distribution at the appropriate confidence level. In this case I would look up the values of the distribution at +- 2.5% (say) to get the 5% critical region as the test is 2-sided. Now say H1:theta>0. I would look up the distribution at 5% as the test is 1-sided. My question is how does testing under H0 distinguish the case H1:theta>0 from theta<0? Ie what effect does the alternative hypothesis have apart from doubling (or halving) the % point you look up for your distribution? I'm sure there is a simple answer! I hope someone can explain to me...
For your 1st case where the alternative hypothesis is H1:Theta>0 you are interested in extreme positive values (Critical value = +1.6449 @ 5%), where H1:Theta<0 you are interested in extreme negative values (Critical value -1.6449 @5%). For H1:Theta=!0 you are interested in both extreme positive and negative values (Critical values +/- 1.96 @5%).
