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Q27Section ST (Statistics (Q11–Q65))27 of 65

Sign test p-value from the observed tail

Let X1,X2,…,XnX_1,X_2,…,X_n be a random sample of size nn (≥11\ge 11) from a population with continuous and strictly increasing cumulative distribution function F(⋅)F(\cdot) with an unknown median MM. To test H0:M=10H_0: M = 10 against H1:M>10H_1: M > 10 at level α\alpha, let the statistic TT denote the number of observations larger than 10. Let t0t_0 be the observed value of the test statistic TT. Consider the test which rejects H0H_0 if T≥cT \ge c. Then the pp-value of the test is

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