Example: a Non-Asymptotic Test for the Support of a Uniform Variable. Testing the Support of a Uniform Variable: Designing a Test. The next few problems cover a test that is not motivated by the CLT. Let X1,…,Xn∼iidUnif[0,θ] where θ is an unknown parameter. Let (R≥0,{Unif[0,θ]}θ>0) denote the associated statistical model. (Here, R≥0 denotes the nonnegative real numbers). "Is θ≤1/2 ?". To do so you formulate a hypothesis test with H0 : θ≤1/2(null hypothesis) H1 : θ>1/2(alternative hypothesis).You also design the test Un = 1(max Xi > 1/2). '1