11.5 Consider an experiment with four groups with eighth values in each. For the
following ANOVA summary table, fill in all the missing results.
Source Degree of freedom Sum of Square Mean Square(Variance) F
___________________________________________________________________________________
Among groups c-1=? SSA=? MSA=80 F=?
with
groups n-c=? SSW=560 MSW=?
Totals n-1=? SSt=?
11.6 You are working with the same experiment as in Problem 11.5
(a). At the 0.05 level of significance, state the decision rule for testing the null
hypothesis that all four groups have equal population means.
(b). What is your statistical decision?
(c). At the 0.05 level of significance, what is the upper tail critical value from
the Students range distribution?
(d). To perform the Tukey-Kramer procedure, what is the critical range?
I'm stuck on this too
11.5 ANOVA Summary Table:
Source Degree of freedom Sum of Square Mean Square(Variance) F
___________________________________________________________________________________
Among groups c-1=3 SSA=? MSA=80 F=?
with
groups n-c=28 SSW=560 MSW=?
Totals n-1=31 SSt=?
To fill in the missing values, we need additional information.
11.6
(a). The decision rule for testing the null hypothesis that all four groups have equal population means at the 0.05 level of significance in an ANOVA is as follows: Reject the null hypothesis if the calculated F-value is greater than the critical F-value.
(b). We do not have the calculated F-value, so we cannot determine the statistical decision.
(c). To find the upper tail critical value from the Student's range distribution at the 0.05 level of significance, we need the degrees of freedom for the numerator and denominator. These degrees of freedom can be calculated based on the number of groups and the sample size, which are not provided in the information given.
(d). To perform the Tukey-Kramer procedure, we need the critical range. The critical range is calculated using the Studentized range distribution and is based on the number of groups and the sample size, which are not provided in the information given.
To answer 11.5:
To fill in the missing results in the ANOVA summary table:
1. Degree of freedom:
- Among groups: c - 1 = 4 - 1 = 3
- With groups: n - c = 8 - 4 = 4
- Totals: n - 1 = 8 - 1 = 7
2. Sum of Square:
- Among groups (SSA): Unknown/Not provided
- With groups (SSW): 560
- Totals (SSt): Unknown/Not provided
3. Mean Square (Variance):
- Among groups (MSA): 80
- With groups (MSW): Unknown/Not provided
4. F:
- Among groups (F): Unknown/Not provided
To answer 11.6:
(a). The decision rule for testing the null hypothesis that all four groups have equal population means at the 0.05 level of significance is to compare the calculated F-value from the ANOVA test with the critical F-value from the F-distribution table with degrees of freedom (numerator: c - 1 and denominator: n - c).
(b). The statistical decision is whether to reject or fail to reject the null hypothesis. This decision is made based on comparing the calculated F-value with the critical F-value.
(c). To determine the upper tail critical value from the Student's range distribution at the 0.05 level of significance, we need to know the degrees of freedom. The degrees of freedom for the Student's range distribution depend on the total number of groups (c). Please provide the total number of groups (c) to calculate the critical value.
(d). To perform the Tukey-Kramer procedure, we need the critical range value. The critical range value depends on the significance level (alpha) and the degrees of freedom for error (denominator degrees of freedom, n - c). Please provide the significance level (alpha) and the degrees of freedom for error (n - c) to calculate the critical range.