Let a random variable X follow a distribution with density f in f0, f1, where f0(x) = begincases 1 & if 0 le x le 1 0 & otherwise endcases and f1(x) = begincases 1 & if 1 le x le 2 0 & otherwise endcases. Let phi be a most powerful test of level 0.05 for testing H0: f = f0 against H1: f = f1 based on X. Then which one of the following options is necessarily correct?

Q20Section ST (Statistics (Q11–Q65))20 of 65

MP test on adjacent supports

Let a random variable $X$ follow a distribution with density $f \in \{f_0, f_1\}$ , where $f_0(x) = \begin{cases} 1 & \text{if } 0 \le x \le 1 \ 0 & \text{otherwise} \end{cases}$ and $f_1(x) = \begin{cases} 1 & \text{if } 1 \le x \le 2 \ 0 & \text{otherwise} \end{cases}$ . Let $\phi$ be a most powerful test of level 0.05 for testing $H_0: f = f_0$ against $H_1: f = f_1$ based on $X$ . Then which one of the following options is necessarily correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.

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