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Spam is the price we pay for being able to easily communicate by e-mail
Spam is the price we pay for being able to easily communicate by e-mail. Does spam affect everyone equally? In a preliminary study, university professors, administrators, and students were randomly sampled. Each person was asked to count the number of spam messages received that day. The results follow. Can we infer at the 2.5% significance level that the differing university communities differ in the amount of spam they receive in their e-mails? Professors Administrators Students 7 5 12 4 9 4 0 12 5 3 16 18 18 10 15
Expert Solution
| Treatment 1 | Treatment 2 | Treatment 3 |
| 7 4 0 3 18 |
5 9 12 16 10 |
12 4 5 18 15 |
The ANOVA procedure tests these hypotheses:
H0: μ1 = μ2 = μ3, all the means are the same
H1: two or more means are different from the others
Calculating Mean and Standard deviation
| Treatments | ||||
| 1 | 2 | 3 | Total | |
| N | 5 | 5 | 5 | 15 |
| ∑X | 32 | 52 | 54 | 138 |
| Mean | 6.4 | 10.4 | 10.8 | 9.2 |
| ∑X2 | 398 | 606 | 734 | 1738 |
| Std.Dev. | 6.9498 | 4.0373 | 6.14 | 5.7842 |
ANOVA TABLE
| SS | df | MS | F | |
|---|---|---|---|---|
| Between groups (or “Factor”) |
SSB = ∑njx?j²−Nx?² | dfB = r−1 | MSB = SSB/dfB | F = MSB/MSW |
| Within groups (or “Error”)* |
SSW = ∑(nj−1)sj² | dfW = N−r | MSW = SSW/dfW | |
| Total* | SStot = SSB + SSW | dftot = N−1 |
r = 3, N = 15
RESULTS -
| Source | SS | df | MS | |
| Between-treatments | 59.2 | 2 | 29.6 | F = 0.86804 |
| Within-treatments | 409.2 | 12 | 34.1 | |
| Total | 468.4 | 14 |
Now, F tabulated at 0.25% level of significance = 5.0958671
Clearly, F calculated < F tabulated as 0.86 < 5.09
Thus, we don't have sufficient evidence to reject the null.
Thus, we conclude that amount of spam does not differ among the three university communities.
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