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A chemical experiment was conducted to test the effects of three methods of purification of water on the pH factor. It was felt that climatic condition also affects the pH of water. The water body was divided into four blocks. A block represented a particular kind of climatic condition. At each block, three areas of equal volume were taken. The three areas at each block were assigned at random to the three methods of purification. The impurities, in ppm, were recorded. If \(P(F\le F_{n_1.n_2.1-\alpha})=1-\alpha\), the critical region to test the equality of mean purification of three methods at a 5% level of significance by randomised block design is:
1. F ≥ F2,6,0.95
2. F ≥ F2,3,0.95
3. F ≥ F2,30.05
4. F ≥ F3,6,0.95

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Correct Answer - Option 1 : F ≥ F2,6,0.95

Given

α = level of significant = 5% = 0.05

R = Row = 3

C = Column = Block = 4

Calculation

n1 = R - 1

⇒ n1 = 3 - 1 

⇒ 2

n2 = (R - 1)(C - 1)

⇒ (3 - 1)(4 - 1)

⇒ n2 = 2 × 3

⇒ n2 = 6

≤ Fn1,n2, 1 - α 

⇒ F≤ F(R - 1),(R - 1)(C - 1),1 - α

⇒ F≤ F2,6,0.95

∴ the critical region to test the equality of mean purification of three methods at a 5% level of significance by randomised block design is F≤ F2,6,0.95

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