Question

The operations department has a business objective of reducing the amount of time to fully update each subscriber's set of messages in a secured email system. An experiment was conducted where 24 subscribers were selected and 3 different messaging systems were used. 8 subscribers were assigned to each system and the update times were measured.

Sys 1 Sys 2 Sys 3

38.8   41.8   32.9
42.1   36.4   36.1
45.2   39.1   39.2
34.8   28.7   29.3
48.3   36.4   41.9
37.8   36.1   31.7
41.1   35.8   35.2
43.6   33.7   38.1
      
A one-way anova was conducted among the 3 different systems. Analyze the results and write a brief summary that indicates your findings. Discuss the reason you selected the particular statsitical test to compare the 3 email systems

Method Null hypothesis All means are equal Alternative hypothesis Not all means are equal Significance level a = 0.05 Equal variances were assumed for the analysis. Factor Information Factor Factor Levels Values 3 System1, System2, System3 Analysis of Variance Source DF Adj SS Adj MS F-Value P-value Factor 2 173.3 86.67 5.14 0.015 Error 21 354.4 16.88 Total 23 527.7

Answer 1

The null and alternative hypotheses are: Ho: Mi = ul2 = 13 Hj: Not all means are equal The value of test statistic is: F=5.14 P-value = 0.015 Conclusion: The p-value of F test is less than 0.05. Hence we reject null hypothesis at 5% level of significance and conclude that the there is significant difference in mean update time among three messaging systems.