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Suppose that (x 1 ....x n ) is a sample from an N(mu o , sigma 2 ) distribution where mu 0 = 0 is

Suppose that (x₁ ....x_n ) is a sample from an N(mu_o, sigma²) distribution where mu₀= 0 is known and sigma²>0 is unknown. Determine the UMP size alpha test for testing H₀ : sigma²= sigma₀² versus H_a: sigma²= sigma₁² where sigma₁²> sigma₀²

Is this test UMP size alpha for H₀ : sigma²= sigma₀² versus H_a: sigma²= sigma₁² ?

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