4 2 points the model p e is specified as follows 0 1 po n 0 1 p a cont
Search for question
Question
4. (2 points) The model {P}e is specified as follows:
• → = {0, 1}.
Po = N(0, 1).
• P₁ = a continuous distribution whose PDF is 1½ exp (-12).
Let X be a sample of size 1, and X
are the following:
~
Po* for an unknown 0* = O. The hypotheses of interest
Ho: 0* = 0, VS. H₁ 0* = 1.
The following information might be helpful: Let & ~ N(0, 1).
•
• The quantile z0.975 is defined as the positive number that satisfies P(§ < 20.975)
P(1)≈0.3374 > 0.3.
=
0.975.
Question: Please show that the following test is the uniformly most powerful test with a
size of 0.05
T = 1 (|X|> 20.975).