Question

Consider the following ANOVA experiments. (Round your answers to two decimal places.)

(a) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄, with n = 23 and α = 0.01.
F ≥

(b) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅, with n = 16 and α = 0.025.
F ≥

(c) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃, with n = 22 and α = 0.01.
F ≥

Answer 1

a) Given that, n=23 no.of treatment=t= 4, α = 0.01

Treatment degrees of freedom= t-1 =4-1 =3

Error degrees of freedom= n-t =23-4= 19

F ratio follows F t-1, n-t , = F3,19, 0.01 = FINV(0.01,3,9)

​ =5.01   (by using MS-Excel)

Critical value= 5.01 and critical region is, F   5.01

b) Given that, n=16 no.of treatment=t= 5, α = 0.025

Treatment degrees of freedom= t-1 =5-1 =4

Error degrees of freedom= n-t =16-5= 11

F ratio follows F t-1, n-t , = F​​​​​​4,11, 0.025 = FINV(0.025,4,11)

​ =4.28    (by using MS-Excel)

Critical value= 4.28 and critical region is, F   4.28

c) Given that, n=22 no.of treatment=t= 3, α = 0.01

Treatment degrees of freedom= t-1 =3-1=2

Error degrees of freedom= n-t =22-3= 19

F ratio follows F t-1, n-t , = F​​​​​​2,19, 0.01 = FINV(0.01,2,19)

​ =5.93 (by using MS-Excel)

Critical value= 5.93 and critical region is, F   5.93