ECC Statistics Worksheet

by | Mar 13, 2022 | Znkxx

Description

Suppose that X1, X2, …, Xin i.i.d N(1, 1).
1. We test hypothesis Ho : u = 0 v.s. Hi : = Mi (M1 + 0). Find the reject
region at level a with a likelihood ratio approach. Calculate the type-I error
and type-II error respectively.
2. Prove that when the null hypothesis above is true, p-value follows uniform
distribution U[0, 1].
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3. Find an a-level test for the problem Ho : M = 0 v.s. Hi :p > 0. Compute
its power function.
4. Find an a-level test for the problem Ho : d = 0 v.s. Hi : M +0. Compute
its power function.

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