alpha is the PROBABILTY of the type 1 error, it's not the error.
Likewise
, which is the same as above.
I am assuming that .25 is the POPULATION st deviation. If it's the sample st dev., we will have a t distribution with 7 degrees of freedom.
In the problem I am given :
n = 8 (sample size)
The random variable follows a normal law with a standard deviation of 0.25
The problem also states that we need to reject [tex]H_0[/Math] if or
I need to find the probability of a type I error.
What I've tried so far: (alpha represents my Type I error)
So I tried to start and find the probability of not in that interval.
which gives me
when I plug my numbers and isolate , i get
It seems to me that this value of Z can't be right since my table only goes to a maximum of 3.09.
As for the rest of the problem, I could use a tip or two about how to find P(u=5) and how to calculate the conditionnal probability.
Thanks
Ok wow I had it wrong, thanks!
(you are correct, it's the standard deviation for the population)
So I end up with P(Z< -1,697) or P(Z>1.697)
which is a probability of 0.0448. Now I guess I add those 2 probabilities and I get alpha? Which is 0.0896 or 8,96%, right?
yes, via a table
you can always get a better approximation of these distributions via an online calculator...
Free Two Tailed Area Under the Standard Normal Curve Calculator
They give me... .0896966
Ok that's great.
For the same problem I also need to find the probability of a type 2 error if is 5.1 (I'll use B to represent the probability of this error)
So I know that B(5.1)=P{accept H_0|H_0 is false}
and
so I end up with P(Z>-2.828) and P(Z<0.567)
that's
(the regions -2.828 to 0 and 0 to 0.567 in the graph of the std normal law)
so P=0.9977-0.5 and 0.7146-0.5
gives me : P=0.4977+0.2146 = 0.7123
This probability seems very high (71.23%) so I'm wondering if I did everything correctly?