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

Size of an extreme-value test

Let X∼Bin⁡(3,θ)X \sim \operatorname{Bin}(3, \theta), where θ∈(0,1)\theta \in (0,1) is an unknown parameter. For testing H0:14≤θ≤34H_0: \frac{1}{4} \le \theta \le \frac{3}{4} against H1:θ<14H_1: \theta < \frac{1}{4} or θ>34\theta > \frac{3}{4}, consider the test ϕ(x)={1if x∈{0,3} 0if x∈{1,2}\phi(x) = \begin{cases} 1 & \text{if } x \in \{0, 3\} \ 0 & \text{if } x \in \{1, 2\} \end{cases}. The size of the test ϕ\phi is __________ (rounded off to two decimal places).

Numerical answer: type the number (no options).

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