Let X (X 1 , X 2 , , X 8 ) be a random sample taken from population has normal distribution N( 0 , sagma 2 ) We want to test H 0 sagma 0 5 against H 1 sagma not equal 0 5 and if the test is reject H 0 if sumation X i 2 5 025 or sumation X i 2 0 4125 Find the size of the critical region and the power function of the test

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Question: Let X=(X 1 , X 2 ,........, X 8 ) be a random sample taken from population has normal distribution N( 0 , sagma 2

Let X=(X₁ , X₂ ,........, X₈) be a random sample taken from population has normal distribution N( 0 , sagma²). We want to test H₀ : sagma = 0.5 against H₁ : sagma not equal 0.5 and if the test is reject H₀ if sumation X_i² > 5.025 or sumation X_i² < 0.4125 .Find the size of the critical region and the power function of the test.

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