GATE 2020 ST – Question 49
In one-way ANOVA Yij=μ+τi+εij,i=1,2,3;j=1,2,3,4, errors are iid N(0,σ²),Στi=0. Test allτi=0 using MST/MSE. If observed ratio is104.45, what is the p-value?
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Correct answer: (A) P(F₂,₉>104.45)
Explanation
Treatment degrees of freedom are3−1=2 and error degrees of freedom12−3=9. Under the null the ratio has F₂,₉ distribution. Large ratios indicate departures from equal means, so the p-value is the upper-tail probability P(F₂,₉>104.45), A.