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 .
a)
dfN = k-1
k = 5
dfN = 4
dFD = k(n-1)
dfD = 5(17-1) = 80
F = 2.49
b)
dfN = k-1
k = 3
dfN = 2
dFD = k(n-1)
dfD = 3(19-1)= 48
F = 4.08
a)
dfN = k-1
k = 5
dfN = 4
dFD = k(n-1)
dfD = 5(17-1) = 80
F = 2.49
b)
dfN = k-1
k = 3
dfN = 2
dFD = k(n-1)
dfD = 3(19-1)= 48
F = 3.23
Other way that you one-way ANOVA
a. dfN = 4
dfD = 12
F =3.26
b. dfN = 2
dfD = 15
F = 3.68
To determine the critical region and critical value for testing the null hypothesis in ANOVA experiments, you need to follow these steps:
Step 1: Determine the degrees of freedom for the numerator (DFN) and denominator (DFD).
For an ANOVA with k groups and n observations per group:
- DFN = k - 1 (number of groups minus 1)
- DFD = n * (k - 1) (total number of observations minus the number of groups)
Step 2: Determine the critical value from the F-distribution table.
For a given significance level (α) and degrees of freedom (DFN and DFD), you need to find the critical value from the F-distribution table. The critical value represents the value of the test statistic beyond which you reject the null hypothesis.
Step 3: Determine the critical region.
The critical region is the area under the F-distribution curve that corresponds to the critical value. If the test statistic falls within this critical region, you reject the null hypothesis.
Now let's apply these steps to the given questions:
(a) In this ANOVA experiment, we have 5 groups and n = 17 observations per group. Therefore, DFN = 5 - 1 = 4 and DFD = 17 * (5 - 1) = 68.
For α = 0.05, we look up the critical value from the F-distribution table using DFN = 4 and DFD = 68. Let's say the critical value is F*.
The critical region can be defined by the inequality F > F*.
(b) In this ANOVA experiment, we have 3 groups and n = 19 observations per group. Therefore, DFN = 3 - 1 = 2 and DFD = 19 * (3 - 1) = 38.
For α = 0.05, we look up the critical value from the F-distribution table using DFN = 2 and DFD = 38. Let's say the critical value is F**.
The critical region can be defined by the inequality F > F**.
Note: It's important to consult a reliable F-distribution table or use statistical software to find the exact critical values for a given significance level (α) and degrees of freedom (DFN and DFD).