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 = 5.42 .

(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 = 2.10. .

(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 3.29. .

To determine the critical region and critical value used in the classical approach for the ANOVA experiments, we need to use the F-distribution. The critical region is the range of values that will lead to the rejection of the null hypothesis, while the critical value is the cutoff value that separates the critical region from the non-critical region.

(a) For the hypothesis Ho: ì1 = ì2 = ì3 = ì4, with n = 19 and á = 0.01, we want to find the critical region and critical value using the F-distribution.

The critical region consists of values that are extreme enough to reject the null hypothesis. In this case, we have four groups or treatments, so the degrees of freedom for the numerator is 4-1 = 3. The degrees of freedom for the denominator is the total sample size minus the number of groups, which is 19-4 = 15.

Consulting an F-table or calculator with degrees of freedom (3,15) and á = 0.01, we find that the critical value is approximately 4.75. Therefore, any F-value greater than 4.75 would lead to rejecting the null hypothesis.

(b) For the hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05, we want to find the critical region and critical value using the F-distribution.

Similar to part (a), the critical region consists of values extreme enough to reject the null hypothesis. Now we have five groups, so the degrees of freedom for the numerator is 5-1 = 4. The degrees of freedom for the denominator is the total sample size minus the number of groups, which is 17-5 =12.

Using an F-table or calculator with degrees of freedom (4,12) and á = 0.05, we find that the critical value is approximately 3.49. Therefore, any F-value greater than 3.49 would lead to rejecting the null hypothesis.

(c) For the hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05, we want to find the critical region and critical value using the F-distribution.

In this case, we have three groups, so the degrees of freedom for the numerator is 3-1 = 2. The degrees of freedom for the denominator is the total sample size minus the number of groups, which is 19-3 = 16.

Using an F-table or calculator with degrees of freedom (2,16) and á = 0.05, we find that the critical value is approximately 3.48. Therefore, any F-value greater than 3.48 would lead to rejecting the null hypothesis.