Mathematics · Statistical Hypothesis Testing

Suppose under the null hypothesis H, X ∼ p, where p(x) = P(X = x) = 1/20, x ∈ {1, 2, …, 20} and under the alternative hypothesis K, X ∼ q where q(x) = P(X = x) = x/210, x ∈ {1, 2, …, 20}. Define two test functions φ and ψ for testing H against K such that φ(x) = 1 if x ≤ 2 and 0 otherwise; and ψ(x) = 1 if x ≥ 19 and 0 otherwise. Which of the following statements is true?