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 = ì5, with n = 17 and á = 0.05.
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, with n = 19 and á = 0.05.
F .
To determine the critical region and critical value in the classical approach for testing the null hypothesis in ANOVA experiments, we need the degrees of freedom and the significance level.
(a) For Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05:
The degrees of freedom for the numerator is k - 1, where k is the number of groups. In this case, k = 5, so the numerator degrees of freedom is 5 - 1 = 4.
The degrees of freedom for the denominator is n - k, where n is the total number of observations and k is the number of groups. In this case, n = 17 and k = 5, so the denominator degrees of freedom is 17 - 5 = 12.
To find the critical value, we need to use a critical value table for the F distribution. Look up the critical value with a numerator degrees of freedom of 4 and a denominator degrees of freedom of 12 at a significance level of 0.05. Let's call this critical value F_crit.
The critical region is the upper tail of the F distribution, so the critical region is F > F_crit.
(b) For Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05:
The degrees of freedom for the numerator is k - 1, where k is the number of groups. In this case, k = 3, so the numerator degrees of freedom is 3 - 1 = 2.
The degrees of freedom for the denominator is n - k, where n is the total number of observations and k is the number of groups. In this case, n = 19 and k = 3, so the denominator degrees of freedom is 19 - 3 = 16.
Again, look up the critical value with a numerator degrees of freedom of 2 and a denominator degrees of freedom of 16 at a significance level of 0.05. Let's call this critical value F_crit.
The critical region is the upper tail of the F distribution, so the critical region is F > F_crit.
By using the degrees of freedom and critical value table for the F distribution, we can determine the critical region and critical value for the ANOVA experiments.