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(greater than)=.
(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(greater than)=
To determine the critical region and critical value for an ANOVA experiment using the classical approach, we need to calculate the F-value and compare it to the critical value from the F-distribution.
(a) For the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and α = 0.05:
1. Calculate the degrees of freedom for the numerator (dfn) and denominator (dfd).
- dfn = k - 1 = 5 - 1 = 4 (k is the number of groups)
- dfd = N - k = n × k - k = 17 × 5 - 5 = 80
2. Look up the critical value in the F-distribution table or use statistical software.
- For α = 0.05 and dfn = 4, dfd = 80, the critical value is approximately 2.50.
3. The critical region is defined as F > critical value.
- The critical region is F(greater than) > 2.50.
(b) For the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and α = 0.05:
1. Calculate the degrees of freedom for the numerator (dfn) and denominator (dfd).
- dfn = k - 1 = 3 - 1 = 2
- dfd = N - k = n × k - k = 19 × 3 - 3 = 54
2. Look up the critical value in the F-distribution table or use statistical software.
- For α = 0.05 and dfn = 2, dfd = 54, the critical value is approximately 3.24.
3. The critical region is defined as F > critical value.
- The critical region is F(greater than) > 3.24.
Please note that the critical values and critical regions may vary depending on the specific degrees of freedom and alpha level used. It's always a good practice to consult a statistical table or use statistical software for accurate and up-to-date values.