GATE 2020 ST – Question 16
In $Y_{ijk}=\mu+\alpha_i+\beta_j+\epsilon_{ijk}$, i=1,2;j=1,2,3;k=1,2,3. Errors are iid N(0,σ²), Σα=Σβ=0, σ>0. SSE is residual sum of squares. Let χ²ν,a denote the(1−a) quantile. Which is a95% confidence interval for σ²?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) $(0,SSE/\chi^2_{14,0.95})$
Explanation
There are18 observations and1+(2−1)+(3−1)=4 fitted parameters, leaving14 residual degrees of freedom. SSE/σ² is χ²14. A one-sided95% upper interval uses the fifth percentile, denoted χ²14,0.95 under the specified upper-tail indexing. Hence(0,SSE/χ²14,0.95), D.