Question
Random samples of two newcomers, two sophomores, two novices, and two elder each fromfour dormitories were asked to rate on a scale from 1 (poor)
Random samples of two newcomers, two sophomores, two novices, and two elder each fromfour dormitories were asked to rate on a scale from 1 (poor) to 10 (excellent) the quality ofthedormitory environmentforstudying.Theresults areshowninthetable.
Year | DormA | DormB | DormC | DormD |
Newcomer | 7 | 8 | 9 | 9 |
5 | 6 | 8 | 9 | |
Sophomore | 6 | 5 | 7 | 8 |
8 | 5 | 8 | 9 | |
Novice | 5 | 7 | 6 | 7 |
4 | 6 | 7 | 8 | |
Elder | 7 | 6 | 7 | 6 |
4 | 8 | 5 | 7 |
Letdorm=Factor A, andstudent year=FactorB.
Youarerequired toconduct a suitableANOVAtest fortheproblemsbelow.
- Calculatethefollowing:
- Sumofsquares and meansquareforFactorA
- Sumofsquares and meansquareforFactorB
- Sumofsquares andmeansquarefortheinteractionbetween FactorAandB
- Totalsumofsquares
- Errorsumofsquaresand mean squareerror
2. Testwhetherthepopulationmeanratingsarethesameforthefourdormitories.
- Statethenullandalternativehypotheses.
- Computetheteststatisticandits-value.
- At 5% significance level, conclude whether the population mean ratings are the sameforthefour dormitories.
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Elementary Statistics Picturing The World
Authors: Ron Larson, Betsy Farber
6th Edition
9780321911216
