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
Could someone help me work out at least one of these and I will try the other ones.
Certainly! I can help you work out one of these ANOVA experiments. Let's start with part (a):
(a) Determining the critical region and critical value for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4, with n = 19 and á = 0.01.
To determine the critical region for this hypothesis test, we need to compare the calculated F-statistic with the critical value from the F-distribution table.
1. Calculate the F-statistic:
To calculate the F-statistic, we need to know the mean square between (MSB) and the mean square within (MSW).
2. Find the degrees of freedom (df):
For this hypothesis test, we have:
- df between = number of groups - 1 = 4 - 1 = 3
- df within = total sample size - number of groups = 19 - 4 = 15
3. Determine the critical value:
Using the significance level (á) of 0.01 and the degrees of freedom, we can find the critical value from the F-distribution table. The critical value is the value at which the area in the upper tail equals the significance level.
4. Compare the calculated F-statistic with the critical value:
If the calculated F-statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Please share the values of MSB and MSW so that we can proceed with the remaining steps and determine the critical region and critical value for part (a) of the ANOVA experiment.