DSE 2012 Ques 39-plzz help

[niki]

Suppose you have a sample of size one from one of the
following densities
H0 : f(x) = 2x   0 <= x<=1
H1 : f(x) = 2 - 2x 0 <= x <= 1
Let alpha and beta denote type I error and type II error, respectively. Find the test
procedure of the form "Reject H0 if x < k" with alpha = 0:09. Find beta for this
test
(a) k = 0:5;  = 0:25
(b) k = 0:5;  = 0:36
(c) k = 0:3;  = 0:16
(d) k = 0:3;  = 0:49
how to do this question..??

[anon_econ]

You have to find k such that P(X<k)=0.09 if X follows the distribution of the null hypothesis. Once you find k you have to find P(X>k) if X follows the distribution of the alternative hypothesis. This basically follows from the definitions of type I and type II errors.

[niki]

thanks a lot vasudha..:)

[laracroft]

Is the answer Option D ??

[niki]

yup..ans is option D..

[Kuldeep]

Hi guys can u help me with q9 and q25 of the dse 2012...

[Ayushya Kaul]

Which test do we use?
The t-test?
What would be the formula for the test? Could anyone show the calculations?

[Ayushya Kaul]

Which test do we use?
The t-test?
What would be the formula for the test? Could anyone show the calculations?

[duck]

Hi Ayushya.. :)

We dont need to use t-test or anything here.
Just use the definition/meaning of type1 and type2 errors.
Type1 error is rejecting the Null given that its true.
It means while finding type1 error, you need to take Null to be true and then, use the test procedure of rejecting null (which is in this case x<k).
So, we've : Type1 error = Integral (2x)dx from 0 to k . And its given Type1 error = 0.09
⇒ Integral (2x) from 0 to k = 0.09
⇒ k =0.3

Now,Type2 error is accepting the null given that alternate hypothesis is true.
So, take Alternate hypothesis to be true and then, use the test procedue of accepting the null (which is x>k).
So, we've: Type2 error = Integral (2-2x)dx from 0.3 to 1
                                = 0.49

[Ayushya Kaul]

You're a life saver :)
Cheers Duck!

[Abhyudaya]

could u pls explain...didnt get it frm ur explaination...I know d theory....