Allison is a chemical engineer who is interested in comparing the hardness of fo

Question

Allison is a chemical engineer who is interested in comparing the hardness of four blends of paint. She applies the different paint blends to multiple pieces of metal, then cures the pieces. She takes six random samples from each paint blend, and measures each sample for hardness. She runs an ANOVA on the data, but spills paint on the output. This results in an incomplete table, as shown

a) Complete the missing entries for the ANOVA table and show work

b) b) Using the ANOVA output, Allison decides that at least one of the paint blends have a significantly different hardness. She then runs a Tukey test and obtains the output on the right. Which blend(s) were significantly different at the = 0.05 level of significance? (If there is a significant difference(s), you must specify the direction). Briefly explain your reasoning.

Source Degree of Freedom Sum of Squares Mean Square F-Value P-value Treatment 3 281.698 Error 20 312.068 Total 23 593.766 Tukey Simultaneous 95% CIs Differences of Means for Hardness Blend 2-Blend1- Blend 3-Blend 1 Blend 4-Blend 1 Blend 3-Blend 2 Blend 4-Blend 2 Blend 4-Blend 3 100 -5 15

Explanation / Answer

b) from above as all interval has value on both side of ) ; except Blennd 4 -blend 2 ; therefore differnce between   Blend 4 -blend 2 is significant and because it is postiive; Blend 4 has higher mean than blend 2/

Source Degree of Freedom Sum of Squares Mean Square F-Value P-value Treatment 3 281.698 93.8993 6.0179 0.0043 Error 20 312.068 15.6034 Total 23 593.766

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