Given the pdf fY (y ) 2y 2 , 0 y Take a sample of size 3 from this pdf Use the statistic Y max to test H 0 5 versus H 1 5 Recall that for n 3 the pdf of Y max is f Ymax (y ) 6y 5 6 , 0 y (a) Find the critical value to give a test of significance 0 05 (b) Suppose 7 What is the Type II error for the test in part (a)

Question: Given the pdf fY (y; ) = 2y 2 , 0 y . Take a sample of size 3 from this pdf. Use

Given the pdf fY (y; θ) = 2y θ2 , 0 ≤ y ≤ θ. Take a sample of size 3 from this pdf. Use the statistic Y_max to test H₀: θ = 5 versus H₁: θ > 5. Recall that for n = 3 the pdf of Y_max is f_Ymax (y; θ) = 6y⁵/ θ⁶ , 0 ≤ y ≤ θ.

(a) Find the critical value to give a test of significance α = 0.05.

(b) Suppose θ = 7. What is the Type II error for the test in part (a).

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