Asked by Anne Marie Kratz on Apr 26, 2024
Verified
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.
Thermal Protection Tiles
Materials used to protect spacecraft from extreme heat during re-entry into the Earth's atmosphere.
Space Shuttle
A reusable spacecraft system used by NASA for human spaceflight missions, including launches into orbit and landings back on Earth.
ANOVA
Short for Analysis of Variance, a statistical method used to compare the means of three or more samples to find significant differences.
- Foster the capability to understand and assess the implications of ANOVA results, such as F-ratio and P-value, in the context of hypothesis testing.
Verified Answer
LP
Lourie PetersMay 01, 2024
Final Answer :
B
Explanation :
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.
Learning Objectives
- Foster the capability to understand and assess the implications of ANOVA results, such as F-ratio and P-value, in the context of hypothesis testing.