Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Tests of Hypotheses
Suppose under the null hypothesis H, X ∼ p, where p(x) = P(X = x) = 1/30, x ∈ {1, 2, … 30} and under the alternative hypothesis K, X ∼ q where q(x) = P(X = x) = x/900, x ∈ {1, 2, … .30}. Define two test functions ϕ and ψ for testing H against K such that,
ϕ(x) = {1, if x ≤ 3, and 0, otherwise} and ψ(x) = {1, if x ≥ 28, and 0 otherwise}.
Which of the following statements are true?
1
The test ϕ(x) is more powerful than ψ(x) for distinguishing H and K.
2
The test ψ(x) is more powerful than ϕ(x) for distinguishing H and K.
3
The critical region for test ϕ(x) is {1,2,3}.
4
Both tests ϕ(x) and ψ(x) are of equal power for distinguishing H and K.