# The null

I am having the hardest time determining what is the null. I have no problem determining the test stat and determining whether it is within or outside of the distribution, i just cant ever get whether the null is what they are looking for ie. there are a hundred pounds of corn in a sack or if the null is the opposite of that or greater than that or whatever… Anyone got any guidelines? I’m missing Q’s cause the null is confusing not because I cant do the math -which is making me nuts because its question semantics AAAARggggghh

Null Hypothesis means something that you are trying to reject with your test. Say for example: You want to test if the sack has 100 lbs of corn, The null hypothesis will state that the amount of corn is not 100. If you are able to reject the null hypothesis, you will be able to prove that there is 100 lbs of corn in the sack. if for example you want to prove that the corn in the sack is less than 100, the null hypothesis will state that the amount of corn is more than 100. rejecting the null will automatically accept the alternate hypothesis.

and to add to that. for the first example the test will be 2 tailed and the null hypothesis will read as H0:Corn<>100. {<> is the sign for not equal to} for the second example the test will be one tailed. H0:Corn>100

vas Wrote: ------------------------------------------------------- > Null Hypothesis means something that you are > trying to reject with your test. > > Say for example: You want to test if the sack has > 100 lbs of corn, > The null hypothesis will state that the amount of > corn is not 100. If you are able to reject the > null hypothesis, you will be able to prove that > there is 100 lbs of corn in the sack. > > if for example you want to prove that the corn in > the sack is less than 100, the null hypothesis > will state that the amount of corn is more than > 100. rejecting the null will automatically accept > the alternate hypothesis. Yikes! I’ll bet the OP is even more confused. You can’t have a null hypothesis that the amount of corn is not equal to 100. With probability 1, the amount of corn is not 100 (it’s 100 + pi/6000 or whatever). That causes you a problem as you will never reject the null because it’s 100% true. Rules about choosing H0: a) H0 never includes ‘<>’ (see above). b) If the problem has no mention of the words “greater” or “lesser” (or synonyms) then it’s always (for example) H0: mu = 5 vs HA: mu <> 5 and never the reverse. c) Often it’s easier to get HA first. HA is the thing you are trying to prove. Then H0 is just everything else. For example, "a drug company wants to show that its new drug decreases blood cholesterol by an average of more than 25 mg/dl so [blah, blah]. " In this case, what we want to show is HA: mu > 25 mg/dl (or you could write HA: mu <= -25 mg/dl if you are into that decrease thing). That means that H0: mu <= 25 mg/dl. d) If there is an equality, always put it in H0. This one doesn’t really matter but convention says that H0 always includes the “=”. e) H0 is always the thing that you start out believing. A jury always starts with H0: defendant is innocent. Usually, H0 is the thing that would cause you no excitement, e.g., defendant doesn’t go to jail and this whole thing was a waste of time, we don’t invest in this stock because there is no earnings effect, I found no new impact of interest rates on bank collapses, etc… Rejecting H0 means you have added new information to the world. Edits: Typos. Geez

Another sort-of rule that only applies to problems in statistics books and CFA exams. Bogus Rule a) HA always looks like it might be true from the data they give you. For example, if they tell you X-bar = 16 and you are trying to decide if you should use HA: mu < 20 or HA: mu > 20 it’s almost certain that it’s HA: mu < 20. The reason is that there is just no testing to be done if your evidence makes it clear that HA is not true so the problem would just be brought to a dead halt. Hypothesis testing is like a courtroom: Data, Test statistic = Evidence H0: Defendant innocent HA: Defendant guilty alpha (or rejection region) = “beyond a reasonable doubt” statistician = Prosecutor (NOT judge). The statistician has an agenda and wants to prove something data mining and exploratory statistics = right to appeal publishing bogus data = prosecutorial misconduct etc… This bogus rule is consistent with the idea that if the police come to a defendant’s house and say “Where were you Monday night when someone shot the deputy?” If you say, “I was giving the Presidential address that was carried by all the networks” then there won’t be a trial. (This is a better response, of course, than “I shot the sheriff but I didn’t shoot the deputy”)