Posted 02 September 2009 - 01:23 PM
on page 550
If I didn't know anything about the tailed tests and I was looking at the probability :
1) p(cured<=80)=5.5% I would accept the null hypothesis
2) p(cured<=80)=0.4% I would reject the null hypothesis
That doesnt make sense.
If p(cured=90) I want to be able to accept (2) particularly as a sign that the null hypothesis is correct.
Is it due to the nature of the accumulated nature of probabilities under the curve? If so then it means that if p(cured<=80)=0.4% then the probability that p(cured=90) cannot be very high. Right? But what if most of the "density" lies between 80 and 90 ? What if p(cured<=80)=0.4% but p(80<=cured<=90)=95%? I guess that is why you say that we expect atleast 5% probability to lie under p(cured<=80). If less we reject the null hypothesis if more we accept it?
But even if p(cured<=80)=0.4% and it is below our significance level and we ought to reject Ho we can make type 1 errors, right? You can't make a type 2 error in the case of Snore Cull because you are already on the brink of rejecting Ho so you can't make a type 2 error, right ?
Question: When you are saying that your alpha or sig level is 5% you really mean that you can accept it if P(cured>=85%) (or 85.1% or 85.08%), right? Why didnt we just do that then? When we do that its P(cured>=85%) on B(100,0.8)(or N(80,16)) comes out to be very small 0.102 so we can right away reject the Ho.
Why don't we just simply find P(cured<85%) and P(cured>=85%) on B(100,0.8)(or N(80,16)) ? I guess we can't do that because we never got any data for cured = 85 ??
So we have to calculate the area under P(cured<=80%) on (claimed data) B(100,0.9)(=0.004) and P(cured>=85%) on (our test data) B(100,0.8)(or N(80,16))(=0.102) ?