In: Statistics and Probability
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 ≥
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 , = F4,11, 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 , = F2,19, 0.01 = FINV(0.01,2,19)
=5.93 (by using MS-Excel)
Critical value= 5.93 and critical region is, F 5.93