) (i) What is a simple hypothesis? Define the terms size and power for a test of one simple hypothesis against another. State and prove the NP Lemma. (ii) There is a single observation of an RV X which has a PDF f(x). Construct the best test of size 0.05 for the null hypothesis Ho: f(x) =; (-1

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) (i) What is a simple hypothesis? Define the
terms size and power for a test of one simple hypothesis against another.
State and prove the NP Lemma.
(ii) There is a single observation of an RV X which has a PDF f(x). Construct the
best test of size 0.05 for the null hypothesis
Ho: f(x) =; (-1<r<l)
against the alternative hypothesis
3
H,: S(x) =÷(1 – x²) (-1<xs1).
Calculate the power of your test.
Transcribed Image Text:) (i) What is a simple hypothesis? Define the terms size and power for a test of one simple hypothesis against another. State and prove the NP Lemma. (ii) There is a single observation of an RV X which has a PDF f(x). Construct the best test of size 0.05 for the null hypothesis Ho: f(x) =; (-1<r<l) against the alternative hypothesis 3 H,: S(x) =÷(1 – x²) (-1<xs1). Calculate the power of your test.
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