A vice president of operations is trying to determine if a new software system will increase productivity for the company. The vice president randomly selects four divisions to participate in the study. Two of the divisions (i. e., groups) receive the new software and two of the divisions (i. e., groups) do not receive the new software. There is a total of 20 teams involved in the study (5 teams per division). As a result, the vice president has a total of 4 groups with an overall sample size of n = 20.
A business analyst collects the productivity data from the 4 groups (20 teams) and conducts an ANOVA test. The business analyst identifies the F-critical value to be 3.24 at the α = 0.05 level of significance. The value for the sum of squares treatment = 135; the value for the sum of squares total = 340. Answer the following 4 questions related to this scenario:
1. The value for the mean square treatment = .
2. The value for the mean square error = .
3. The value for the F-test statistic = .
4. Is there a significant difference in productivity (α=0.05) between at least two groups?