Question

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:

24. Using Scenario 4 above, the value for the mean square treatment =

25. Using Scenario 4 above, the value for the mean square error =

26. Using Scenario 4 above, the value for the F-test statistic =

27. Using Scenario 4 above, is there a significant difference in productivity (α=0.05) between at least two groups?  

Answer 1

For ANOVA, Hull Hypothesis, to : There is no significant difference in the meant productivity across four groups in eo l = M2 = 43 = ly Alternative Hypothesis, Has There exists at least oule group for which mit lig for atleast one i tj 24. 1 U Mean Square Treatment = len & Squares Treatment kol where k ů the no. of breaturents = 4 So, Mean Square Treatineuil = 135 = 45. 25. 1. Mean Square Error = Smer of squares Erros n-k where in ů the nood cleans = 20 so, Mean Square Ersas - Slund Squaves Total - Sund Squares Treatenent - 20-4 Miau &quous Errus = 340 -135 = 205 Mean Square Ersor = 13-8125 So, me 16 16 26. F- statistics = Mean Square Treatment = Mean Square Error 45 12.8125- F-itatistici = 3.512195 27. Hot do 0.05 and degrees of feeean Ck-len-k) = ( 3,16), The critical value of F = 3.239 sunce, F = 3.51219573 239 so we yict Ho at's % level & conclude that there is siguificant difference us productivity beltween at least a groups. Scanned with CamScanner Do Drop a like & stay Safe!