An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P-value
Method 985535.907
Error 276844.275
Total 1262380.182
A)MST = 492767.954; MSE = 19774.591; F-Ratio = 24.919; Yes,reject H0 using α = 0.05.
B)MST = 492767.954; MSE = 23070.356; F-Ratio = 21.359; Yes,reject H0 using α = 0.05.
C)MST = 328511.969; MSE = 23070.356; F-Ratio =14.240; Yes,reject H0 using α = 0.05.
D)MST = 328511.969; MSE = 19774.591; F-Ratio =16.613; Yes,reject H0 using α = 0.05.
E)MST = 492767.954; MSE = 21295.713; F-Ratio = 23.139; Yes,reject H0 using α = 0.05.

Question

Quizplus · Accepted Answer

MST (Mean Square Treatment) is calculated by dividing the sum-of-squares for the method by its degrees of freedom (df). Here, df for method is 3 - 1 = 2 (since there are three methods), so MST = 985535.907 / 2 = 492767.954. MSE (Mean Square Error) is calculated by dividing the sum-of-squares for error by its degrees of freedom. Here, df for error is 15 - 3 = 12 (since there are 5 people per method and 3 methods), so MSE = 276844.275 / 12 = 23070.356. The F-ratio is MST / MSE = 492767.954 / 23070.356 = 21.359. Since the F-ratio is significant (based on the p-value, which is not directly given but implied to be less than α = 0.05), we reject H0.

An Industrial Engineer Wants to Test the Effect of Three