GATE 2021 ST – Question 62

Testing of Hypotheses · Most Powerful and Uniformly Most Powerful Tests · 2 marks · Numerical answer

A size-100 sample from N(μ,9) has mean 5.608. Given Φ(1.96)=.975 and Φ(1.64)=.95,find the p-value of the UMP unbiased test μ=5.02 against μ≠5.02,to three decimals.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.045 to 0.055

Explanation

Known standard deviation is 3,so the sample mean’s standard error is 3/10=.3. The observed Z=(5.608−5.02)/.3=1.96. The two-sided p-value is 2[1−Φ(1.96)]=2·.025=**0.050**.

More Most Powerful and Uniformly Most Powerful Tests questions

GATE 2021 ST Q63 – X takes 7,8,9,10. Under p₀ the probabilities are .90,.05,.04,.01;under p₁ they are…
GATE 2026 ST Q21 – For testing H₀ against H₁ at level α∈(0,1), which statement holds?
GATE 2026 ST Q34 – X is uniform on (θ,θ+1),θ∈ℝ. For testing H₀:θ≤0 against H₁:θ>1, let β be the power of a…
GATE 2026 ST Q45 – An iid sample n>1 has f β(x)=βe(−x)(1−e(−x))(β−1),x>0,β>0. Test H₀:β=1 against H₁:β>1 at…
GATE 2026 ST Q57 – From a single observation, test H₀:θ=1 against H₁:θ≠1 at level 0.05. For which density…
GATE 2026 ST Q65 – A single X has density 2x/θ² on 0<x<θ, zero otherwise,θ>0. Test H₀:θ≤1 against H₁:θ>1 at…

All Most Powerful and Uniformly Most Powerful Tests questions →