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.After collecting the data and analyzing the results,he reports that the F-ratio is 3.097.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?
A)p = 0.0827.Reject H0 using α = 0.05.
B)p = 0.0827.Do not reject H0 using α = 0.05.
C)p = 0.0827.Reject H0 using α = 0.01.
D)p = 0.208.Do not reject H0 using α = 0.05.
E)p = 0.0827.Do not reject H0 using α = 0.10.

Question

Quizplus · Accepted Answer

To find the P-value, we need to use an F-distribution table or calculator. Since there are three compounds, the degrees of freedom for the numerator is 2, and the degrees of freedom for the denominator is 12 (total number of tiles - number of groups). Using α = 0.05 as the significance level, we find that the critical F-value is 3.89. Since the calculated F-ratio (3.097) is less than the critical F-value, we do not reject the null hypothesis. Therefore, the P-value is greater than 0.05. The only choice that matches this conclusion is B: p = 0.0827.

A Mechanical Engineer Is Studying Bonding Issues with the Thermal