Consider the following ANOVA experiments. (Give your answers correct to two decimal places.)
(a) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4, with n = 19 and á = 0.01.
F
(b) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05.
F
(c) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05.
F
To determine the critical region and critical value for each ANOVA experiment, we need to use the F-distribution and the significance level (α).
(a) For the null hypothesis Ho: μ1 = μ2 = μ3 = μ4, with n = 19 and α = 0.01:
The critical region is in the right tail of the F-distribution, as we are looking for a higher value of F. The degrees of freedom for the numerator (df1) is 4-1 = 3, and the degrees of freedom for the denominator (df2) is (19-1) * 4 = 72.
Using the F-table or a statistical software, we find the critical value to be F(3, 72, 0.01) = 5.99.
(b) For the null hypothesis Ho: μ1 = μ2 = μ3 = μ4 = μ5, with n = 17 and α = 0.05:
The critical region is in the right tail of the F-distribution, as we are looking for a higher value of F. The degrees of freedom for the numerator (df1) is 5-1 = 4, and the degrees of freedom for the denominator (df2) is (17-1) * 5 = 80.
Using the F-table or a statistical software, we find the critical value to be F(4, 80, 0.05) = 2.70.
(c) For the null hypothesis Ho: μ1 = μ2 = μ3, with n = 19 and α = 0.05:
The critical region is in the right tail of the F-distribution, as we are looking for a higher value of F. The degrees of freedom for the numerator (df1) is 3-1 = 2, and the degrees of freedom for the denominator (df2) is (19-1) * 3 = 54.
Using the F-table or a statistical software, we find the critical value to be F(2, 54, 0.05) = 3.19.
So, for (a) the critical region is F > 5.99 with df1 = 3 and df2 = 72, for (b) the critical region is F > 2.70 with df1 = 4 and df2 = 80, and for (c) the critical region is F > 3.19 with df1 = 2 and df2 = 54.