Quants - t-stats

Hey fellas, Consider this :Samples are drawn from normally distrubuted populations. Sample 1 : Mean - $50 , Std Deviation - $5 , n=25 Q) Null Hypothesis : Mean of Sample 1 <= $48 versus Alternate Hypo : Mean of Sample 1 > $48 . At 5% level of significance , the null hypothesis : a . Cannot be rejected. b . Should be rejected. For solving this we have to use t - stat .The level of significance is 5% , so should I look for 0.05 or 0.025 in the Student’s T - Distribution table ? Refer to Q 17 Pg 333 , Schweser 2008 Book 1. Regards, Gaurav

For 0.5 (since this is a one tail test), at 24 (that is n-1) degrees of freedom. This would be 1.711.

depends on 1-tail vs. 2-tail test. for a 2-tail test – you have .025 (2.5%) in each tail so the area left in the middle is 95%. for a 1-tail test - you have the entire .05 (5%) in one tail, so the area left to the right of that tail is the 95%. Also remember – your NULL hypothesis definition will always have the = sign in it.

And in this case, it’s a 1-tail test. For t-statistics (i.e., tests about a mean) you can tell 1-tail tests from 2-tail tests by looking at Ha (alternative hyp). If Ha contains >, or < it’s a 1-tail test. If it contains <> (not equal) it’s a 2-tail test.

All the one tail test and two tail test depends on the Alternate Hypothesis. see If Case 1: H0:u1=u2 H1: u1 != u2 Then it will be two tail test Case 2: If H0:u1<=u2 H1: u1 >u2 Then it will be right tail test Case 3: If H0:u1>=u2 H1: u1< u2 Then it will be left tail test… According to your problem,it matches the Case 2 so it will be Right tail test.

Yes, the last guy is more clearer… If it has an equality sign, it is a two tail. If it has a < or > sign, it is a one tail. Hope it helps!

So for one tail test, the null hyphothesis must always have = sign, even if not stated in the question? How id the question said that the alternative hypothesis is >=x, does that mean the null will be

From a technical point of view, Ho: mu > b vs Ha: mu <= b is the same as Ho: mu >= b vs Ha: mu < b

Always make sure you are 100% sure of how you distinguish a one tail from a two tail… only when you are sure you won’t get this wrong again you should move on.