Mathematics · Non-Parametric Tests
Let {Xn : n ≥ 1} be i.i.d. observations with a common continuous distribution function F(x - θ), where θ is the unique median of F. Define Yi = 1 if Xi > 1 and Yi = 0 if Xi ≤ 1, and let Sn = ∑i=1n Yi. For testing H0: θ = 1 against H1: θ > 1, which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Sn follows a Binomial(n, 0.5) distribution under H0✓
- 2The test based on Sn is distribution-free under H1
- 3The right-tailed test based on Sn is biased
- 4The sequence of right-tailed tests based on Sn as n → ∞ is inconsistent
Correct answer
Sn follows a Binomial(n, 0.5) distribution under H0
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