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Q46Section ST (Statistics (Q11–Q65))46 of 65

Sign test for a median

Let X1,X2,…,X5X_1, X_2, \dots, X_5 be random observations from a continuous distribution. Let θp\theta_p be the pp-th population quantile. Consider the following hypotheses H0:θ1/2=2.5H_0: \theta_{1/2} = 2.5 against H1:θ1/2>2.5H_1: \theta_{1/2} > 2.5. Let X(r)X_{(r)} denote the rr-th order statistic of the given observations. Then which of the following is a critical region of a level 0.05 test?

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