Suppose that T_1 is a alpha ∗ 100% lower confidence limit for theta and T_2 is a alpha ∗ 100% upper confidence limit for theta. Further assume that P(T_1<T_2)=1. Find a (2alpha-1)∗100% confidence interval for theta

atgnybo4fq

atgnybo4fq

Answered question

2022-11-17

About intervals of confidence
Suppose that T 1 is a α 100 % lower confidence limit for θ and T 2 is a α 100 % upper confidence limit for θ. Further assume that P ( T 1 < T 2 ) = 1. Find a ( 2 α 1 ) 100 % confidence interval for θ
I thought that ( T 1 , T 2 ) was a α 2 100 % confidence interval, but it is only if T 1 , T 2 are independents (correct?)

Answer & Explanation

motylowceyvy

motylowceyvy

Beginner2022-11-18Added 19 answers

Step 1
Your statement about α 2 looks peculiar given that you know P ( T 1 < T 2 ) = 1.
Step 2
The events T 1 > θ and T 2 < θ are not independent, since if T 1 > θ then Pr ( T 2 < θ ) = 0. Indeed T 1 > θ and T 2 < θ are almost surely mutually exclusive
Hint: You should reconsider Pr ( T 1 θ T 2 ) in the light of this

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?