The computer operations department had a business objective ofreducing the amount of time to fully update each subscriber's setof messages in a special secured email system. An experiment wasconducted in which 23 subscribers were selected and three differentmessaging systems were used. Eight subscribers were assigned toeach system, and the update times were measured as follows:
| System A | System B | System C |
| 38.8 | 41.8 | 36.9 |
| 42.1 | 36.4 | 36.1 |
| 45.2 | 39.1 | 39.2 |
| 34.8 | 28.7 | 35.6 |
| 48.3 | 36.4 | 41.9 |
| 37.8 | 36.1 | 31.7 |
| 41.1 | 35.8 | 35.2 |
| 43.6 | - | 38.1 |
Given Sample Means: x?a = 41.46, x?b = 36.33, x?c = 35.84, GrandMean = 38.29
Given Sample Standard Deviations: sa = 4.32, sb = 4.00, sc =3.02, S = 4.34
A) At the 0.05 level of significance, is there evidence of adifference in the variance of the update times between Systems Band C? (Show your work: hypotheses, test statistic, critical value,and decision).
B) Fill out the following summary table for One-Way ANOVA:
| Source of Variation | SS | df | MS | F |
| Among Groups | | | | |
| Within Groups | | | 14.54 | - |
| Total | | 22 | - | - |
C) Using the Tukey-Kramer method, determine which pair of thedesigns have the difference in mean distances at the 0.05 level ofsignificance by filling out the following table (the upper-tailcritical value from the studentized range distribution with 3 and20 degrees of freedom as Q? = 3.578)
| Pair (i,j) | |Xbari -Xbarj | | Comparison (> or <) | Critical Range | Difference (Yes or No) |
| (A,B) | | | | |
| (A,C) | | | | |
| (B,C) | | | | |
