Question

e. Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal places. Round F to two decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total f. At the α-.05 level of significance, test whether the means for the three treatments are equal The p-value is less than.01 What is your conclusion? Select

Answer 1

k = number of groups = k = 3 and N = total observations = 18

The Overall Mean = (159 + 142 + 134) / 3 = 145

DF Between = k - 1 = 3 - 1 = 2

DF error = N - k = 18 - 3 = 15

(a) SS between = SUM [n * ( $\bar{x}_i$ - Overall Mean)²] = 6 * (159 - 145)² + 6 * (142 - 145)² + 6 * (134 - 145)² = 1956

(b) MS between = SS between / DF between = 1956/2 = 978

(c) SS error = SUM [(n - 1) * Variance] = (5 * 311.6) + (5 * 91.6) + (5 * 151.6) = 2774

(d) MS error = SS error / DF error = 2774 / 15 = 184.9

(e) The ANOVA Table is as Below.

Source	SS	DF	Mean Square	F
Between	1956	2	978	5.29
Within/Error	2774	15	184.9
Total	4730	17

(f) The p value for F = 2.29, DF between = 2, DF error = 15 is 0.0183

Therefore 0.01 < p value < 0.05

Conclusion: Since p value is < 0.05, Reject H0.