Question

Note: When answering review questions in this chapter and the next two ANOVA chapters, you can bypass the customary step-by-step hypothesis testing procedure and sum- marize your results with an ANOVA table, as in Table 16.6. 16.9 Given the aggression scores below for Outcome A of the sleep deprivation experi- ment, verify that, as suggested earlier, these mean differences shouldn't be taken seriously by testing the null hypothesis at the .05 level of significance. Use the com- putation formulas for the various sums of squares and summarize results with an ANOVA table. HOURS OF SLEEP DEPRIVATION ZERO TWENTY-FOUR FORTY-EIGHT 3 2 5 8 4 7 6 6 5 6 4 Grand mean = 5 4 Group mean:

Answer 1

US Ha: Not all means are equal Ho: M. = M = M3 Hourg ob sleeb Debrivation Zero Twenty for Forry-fish 3 2 4 S 8 4 7 6 6 sum 15 18 12 5 6 4 Mean 83 116 56 Wor first Compute Grand mea total need to we GE {{xis - 15+ 18+ 12 =45 G = 45 Gorrection factor (CF) Correction factor CC.F) is G² 9 The us² Gif - - 225 CS Scanned with CamScanner

... Cof=225 Valles y Now, the total Sum of Sluared XS 44184 exist = 83 +116 +56 { x = 295255 Total Sum ob Squares ! total sum of selares & (TSS) is The TSS 11 { xi-C.F 255 = 25 - 225 TSS = 30 CS Scanned with CamScanner

s.Swithin Sun of Squareg between Samples (SS between) 2 C. SS, between 225 Is 18 + 3 225 = 231 Here Ti is ith Sample ss between 6 total CSS within) Sum of Salary With in the samples TSS SS between 30 - 6 11 SS cathin 24 2 30/22 - Total degrees of freedom = n1 = 9-18 Degrees of freedom between Samples Degrees of feedom within samples = 8-2=6 cs Scanned with CamScanner

Mean sum Source of Variation sum of Squares Degree of freedo ot Sruary Fratio 6 Between samply 2 3 F = 20:16 with in samples 24 6 4 * * Total 30 8 Test Stalistic; m. s between F = mis 20.75 m.s within Fs 0.75 Rejection region : dfia 28 df = 2. Reject He it F > Fa 5.143 cs Scanned with CamScanner

Decision about Ho that Since it is observed F=0.75 < F = 5.143 с it is then that fail to reject Concluded hypothesis the null Conclusion: fail to reject the null hypothesis evidence to Therefore, there is not enough claim that all three elhal at d.o.os not Population means are CS Scanned with CamScanner