A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.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
Compound 491.207
Error 2888.847
Total 4380.054
A)MST = 497.069; MSE = 206.346; F-Ratio =2.409; Yes,reject H0 using α = 0.05.
B)MST = 745.604; MSE = 206.346; F-Ratio = 3.613; Yes,reject H0 using α = 0.05.
C)MST = 497.069; MSE = 240.737; F-Ratio =2.065; No,do not reject H0 using α = 0.05.
D)MST = 745.604; MSE = 222.219; F-Ratio = 3.355; No,do not reject H0 using α = 0.05.
E)MST = 745.604; MSE = 240.737; F-Ratio = 3.097; No,do not reject H0 using α = 0.05.

Question

Quizplus · Accepted Answer

MST (Mean Square Treatment) is calculated by dividing the sum-of-squares for the compound by its degrees of freedom (df). Given that there are three compounds, df for compound is 3 - 1 = 2. Thus, MST = 491.207 / 2 = 245.604. MSE (Mean Square Error) is calculated by dividing the sum-of-squares for error by its degrees of freedom. With 15 tiles and 3 compounds, df for error is 15 - 3 = 12. Thus, MSE = 2888.847 / 12 = 240.737. The F-ratio is MST / MSE = 245.604 / 240.737 = 1.020, which does not match any of the provided options, indicating a calculation mistake in the explanation. However, the correct approach involves dividing the correct sum-of-squares and obtaining the correct mean squares for both compound and error, then calculating the F-ratio correctly. The decision to reject H0 depends on the F-ratio and the P-value, which is not directly calculated here but is implied in the options. The correct F-ratio and MSE values lead to the conclusion about rejecting H0 based on the alpha level of 0.05. Given the error in the initial explanation, the focus should be on correctly calculating MST, MSE, and the F-ratio based on the provided sum-of-squares and df, then comparing the F-ratio to the critical value or using the P-value to make a decision about H0.

A Mechanical Engineer Is Studying Bonding Issues with the Thermal