hypothesis testing, uniform distribution Watch

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3. Consider a random sample (X 1 ,...,X n ) from a Uniform distribution on the interval
(0,θ), where θ > 0 is unknown. We want to test
H 0 : 3 ≤ θ ≤ 4 vs H 1 : θ < 3 or θ > 4
Use as test statistic Y = max Xi . Assume that the acceptance region is given by
2.9 ≤ Y ≤ 4 and the critical region is Y > 4 or Y < 2.9. Determine the size of the
test and the power function.

am i correctly in calculating the size of the test as 0 since under the null you cannot accept the alternative hypothesis

and the power of the test would be 1-b(t), where b(t) is the probability of accepting the null given the alternative is true, which is only >0 if h1 is θ < 3 and 2.9 ≤Y<3.

i suppose the probability of the max Xi being in 2.9 ≤Y<3 is the probability of all X 1 ,...,X n being in 2.9 ≤ <3 which can be calculated from a cdf of a uniform distribution i dunno

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