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Q45Section C (Section C)45 of 60

Type I error of a uniform max test

Let X1,X2,…,X10X_1,X_2,…,X_{10} be i.i.d. U(0,θ)\mathrm{U}(0,\theta) random variables, where θ>0\theta>0 is unknown. For testing the null hypothesis H0:θ=1H_0:\theta=1 against the alternative hypothesis H1:θ=0.9H_1:\theta=0.9, consider a test that rejects H0H_0 if X(10)=max⁡{X1,…,X10}<0.8X_{(10)}=\max\{X_1,…,X_{10}\}<0.8. Then the probability of type I error of the test is equal to __________ (round off to 2 decimal places)

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