Question

Assume that 18 subjects received one of three treatments and produced the data reported in Data Set B. Conduct a one-way ANOVA to see if the means of the three treatments are different on a statistically significant level, using a two-tailed alpha of .05. Complete an ANOVA table reporting the relevant SS, df, MS, and F. Also remember to include your critical value and whether you would reject your null hypothesis. (20 points)

Data Set B Treatment 1 Treatment 2 Treatment 3 50 60 70 55 60 65 80 70 90 45 65 55 85 70 55 35 40 45

PLEASE NO EXCEL! THANK YOU :)

Answer 1

Total X1 X2 X3 70 50 60 180 65 55 60 180 90 70 80 240 45 55 65 165 70 55 85 210 45 35 40 120 6 6 18 n- Total-EX 360 365 370 1095 grand mean Xgrand Average=X-EX/n= 60.0000 60.8333 61.6667 60.8333 Total=EX 24100 23125 23300 s(Ex(EX)/n)/(n-1) = 500,0000 184.1667 96.6667 Total observation 18 N= number of groups k= 3 between groups degree of freedom df k-1 2 within groups degree of freedom dfw-N-k = 15 dfTotal Total degree of freedom 17 - (n-1)*s n (X-Xran) n 4.17 1 6 60.0000 500.000 2500.00 2 6 60.8333 184.167 0.00 920.83 6 61.6667 96.667 4.17 3 483.33 total 8.3333 3904.1667 n(X-Xran 2(n-1)*s2= sum of square between groups-SSG = 8.3333 sum of square within groups SSE = 3904.1667 total sum of square SSG+SSE -SST= 3912.5000 Summary table Source of variation SS df MS between 8.333 2.0000 4.17 0.02 within 260.28 3904.167 15.0000 total 3912.500 17.0000

as critical value at (2,15) degree of freedom and 0.05 level =3.68 is greater than test statistic 0.02, we can not reject null hypothesis,

We do not have evidence at 0.05 level to conclude that means of the three treatments are different