StatisticsdrillOne-way ANOVA F statistic
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
A plant compares the daily output of three shifts. Group summaries (units): Morning: n = 11, x̄ = 139.5, s = 12.4; Afternoon: n = 6, x̄ = 136.5, s = 10.9; Night: n = 12, x̄ = 146.4, s = 11.9. Compute the one-way ANOVA F statistic for H0: all three means are equal, then decide at α = 0.05. Round to 2 decimal places.
What this problem teaches
The formula: F = MSB / MSW = [SSB / (k - 1)] / [SSW / (N - k)]. F compares spread between group means with spread inside the groups. Weight each group mean by its n when the groups are unequal in size; the unweighted average of the means is not the grand mean.
A hint if you get stuck
Grand mean = Σ n_j x̄_j / N. SSB = Σ n_j (x̄_j - grand mean)², SSW = Σ (n_j - 1) s_j². F = [SSB / (k - 1)] / [SSW / (N - k)].
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