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Q63Section ST (Statistics (Q11–Q65))63 of 65

Type-I error of a max test

Let X1,X2,X3,X4X_1,X_2,X_3,X_4 be a random sample of size 4 from a population having uniform distribution over the interval (0,θ)(0,\theta), where θ>0\theta > 0 is an unknown parameter. Let X(4)=max⁡{X1,X2,X3,X4}X_{(4)} = \max\{X_1,X_2,X_3,X_4\}. To test H0:θ=1H_0: \theta = 1 against H1:θ=0.1H_1: \theta = 0.1, consider the critical region that rejects H0H_0 if X(4)<0.3X_{(4)} < 0.3. Let pp be the probability of the Type-I error. Then 100p100 p equals ____________ (rounded off to two decimal places).

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