Question

Message Therapy

Does e-mail spam affect everyone at the University of Ottawa equally? To answer this, a small study was conducted by randomly selecting 10 each of professors, administrators and students. Each person was asked to count the number of spam messages received on a given day. Some of the results are presented below.

SUMMARY Count Average Variance 14.3 12.1 6.6 Groups Professors Administrators Students 10 10 10 63.34 38.10 12.04 ANOVA Source of Variation df MS Between Groups Within Groups Total 37.83 1336.0 29

a) Fill in the correct values for the missing quantities in the ANOVA table above. Show your computations reporting a maximum of two decimal places.

b) Carry out a hypothesis test to determine whether the mean amounts of e-mail spam are not all equal across the different university communities. Please provide:

-Hypotheses

-Value of test statistic, to two decimal places

-The critical value for the corresponding test statistic at α = .05 (include degrees of freedom)

-Exact p-value using software

-Conclusion; don’t simply say “reject” or “do not reject”; include a statement with practical meaning

c) What assumption of the ANOVA model can be examined with the information provided in the summary table above? Explain briefly. Assuming the assumption is warranted, show how the MSE is calculated using the sample variances.

d) Suppose one of the students received 20 spam e-mails. Explain how this would enable you to question another key assumption of the ANOVA model. What would you conclude?

e) What is the margin of error associated with the Bonferroni method for multiple paired comparisons between the population means? Assume a family confidence level of 95%. Using the Bonferroni method, determine which pairwise differences are or are not statistically significant. What do you conclude? Show your work.

f) If instead of considering only three university communities, we consider five. For example, part- time instructors, full-time instructors, administrators, undergraduate students and graduate students. How many pairwise comparisons are possible?

g) Suppose we now ask each group of participants to count the number of spam e-mail messages every day for a seven-day period. Identify this experimental design. Explain briefly.

Answer 1

o)ANOV A s Sdf 314 592 aithi 1021 2 MS 1ST, 29 s 3T-83 4.6 Totad 1336 02 Fニ MSDet woon// M sasthǐ一ー416 Test statistic, F 416 Critica valus Foos (significan t) İS 0:0 26 6 F -4, 16 pvaluator Ther s enouph ewdoues to concluda at weau the difrareut univepsity cowities (c) age caw exaurį ne ta Rassuurfti on of equal MSE 27