A sample of size n taken from a normal population with a known variance of o² = 9.7969 is used to test Ho : μ = μo against H₁ : μ = μ₁ where #₁> #o. Use the Neyman-Pearson Lemma to produce a test statistic and the corresponding most powerful critical region at the a level of significance for a given a.
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Working with the Neyman-Pearson Lemma.
(a) A sample of size n taken from a normal population with a known variance of σ
2 = 9.7969 is used to
test H0 : µ = µ0 against H1 : µ = µ1 where µ1 > µ0. Use the Neyman-Pearson Lemma to produce
a test statistic and the corresponding most powerful critical region at the α level of significance for a
given α.
(b) Suppose the
at the 1% level of significance for testing H0 against H1. en compute the power of the test.
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