16 independent normal observations were collected from a population i mean u and known variance o? = 4. We want to test

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16 independent normal observations were collected from a population
with unknown mean u and known variance o?
4. We want to test
Ho : µ = 0 vs Ha : µ #0
||
а
(a)
(b)
the level of significance (Here is the sample mean of x's).
Write down the GLRT rejection region for the problem.
Consider an alternative test that rejects Họ if |¤| > 1. Compute
(c)
alternative u = 1.5. Which test seems better w.r.t. the power at u = 1.5 ?
Compute the power of test from part (a) and part (b) for the
Transcribed Image Text:16 independent normal observations were collected from a population with unknown mean u and known variance o? 4. We want to test Ho : µ = 0 vs Ha : µ #0 || а (a) (b) the level of significance (Here is the sample mean of x's). Write down the GLRT rejection region for the problem. Consider an alternative test that rejects Họ if |¤| > 1. Compute (c) alternative u = 1.5. Which test seems better w.r.t. the power at u = 1.5 ? Compute the power of test from part (a) and part (b) for the
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