hypothesis testing, uniform distribution Watch

Calculator fx
Badges: 1
Rep:
?
#1
Report Thread starter 4 years ago
#1
3. Consider a random sample (X 1 ,...,X n ) from a Uniform distribution on the interval
(0,θ), where θ > 0 is unknown. We want to test
H 0 : 3 ≤ θ ≤ 4 vs H 1 : θ < 3 or θ > 4
Use as test statistic Y = max Xi . Assume that the acceptance region is given by
2.9 ≤ Y ≤ 4 and the critical region is Y > 4 or Y < 2.9. Determine the size of the
test and the power function.

am i correctly in calculating the size of the test as 0 since under the null you cannot accept the alternative hypothesis

and the power of the test would be 1-b(t), where b(t) is the probability of accepting the null given the alternative is true, which is only >0 if h1 is θ < 3 and 2.9 ≤Y<3.

i suppose the probability of the max Xi being in 2.9 ≤Y<3 is the probability of all X 1 ,...,X n being in 2.9 ≤ <3 which can be calculated from a cdf of a uniform distribution i dunno
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 31 Jul '19
  • Staffordshire University
    Postgraduate open event - Stoke-on-Trent campus Postgraduate
    Wed, 7 Aug '19
  • University of Derby
    Foundation Open Event Further education
    Wed, 7 Aug '19

Are you tempted to change your firm university choice on A-level results day?

Yes, I'll try and go to a uni higher up the league tables (155)
17.61%
Yes, there is a uni that I prefer and I'll fit in better (76)
8.64%
No I am happy with my course choice (522)
59.32%
I'm using Clearing when I have my exam results (127)
14.43%

Watched Threads

View All