Use to following results to complete an analysis of variance table, find the critical value, and determine whether to accept or reject the null hypothesis that there is no difference in mean across the groups given ? = .05.
We calculate
BSS = 10 * (540.3 - 543.6)2 + 16 * (602.9 - 543.6)2 + 17 * (489.8 - 543.6)2 = 105578.2
WSS = (10 - 1) * 46.42 + (16 - 1) * 47.42 + (17 - 1) * 48.92 = 91337.4
F = (BSS / (k-1)) / (WSS / (n-k)) = (105578.2 / (3 - 1)) / (91337.4 / (43 - 3)) = 23.1
The critical F value is F.05,2,40 = 3.23. The observed value vastly exceeds this, so we clearly reject the null hypothesis and conclude that the means differ across the groups.
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