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.

1. Calculatethefollowing:
   1. Sumofsquares and meansquareforFactorA
   2. Sumofsquares and meansquareforFactorB
   3. Sumofsquares andmeansquarefortheinteractionbetween FactorAandB
   4. Totalsumofsquares
   5. Errorsumofsquaresand mean squareerror

2. Testwhetherthepopulationmeanratingsarethesameforthefourdormitories.

1. Statethenullandalternativehypotheses.
2. Computetheteststatisticandits-value.
3. At 5% significance level, conclude whether the population mean ratings are the sameforthefour dormitories.