Instructions:

Please make sure you use the assignment template and outline the answer to the question as follows.

Section $1$: Problem Statement

Section $2$: Assumptions

Section $3$: Analysis

Section $4$: Conclusion

Section $5$: Recommendations

You are an industrial engineer responsible for a process which produces trusses used for supporting various sections used in bridge construction. You perform a study of the various material properties. One of the key ones being axial stiffness of the plates. Your study yielded the following observations on the axial stiffness index $($kips$/$in$.)$ for several plate lengths produced at a facility.

$\backslash$table$[[,$Stiffness in Samples$],[\backslash$table$[[$Plate$],[$Length:$]],1,2,3,4,5,6,7],[4,309\mathrm{.}2,409\mathrm{.}5,311\mathrm{.}0,326\mathrm{.}5,316\mathrm{.}8,349\mathrm{.}8,309\mathrm{.}7],[6,402\mathrm{.}1,347\mathrm{.}2,361\mathrm{.}0,404\mathrm{.}5,331\mathrm{.}0,348\mathrm{.}9,381\mathrm{.}7],[8,392\mathrm{.}4,366\mathrm{.}2,351\mathrm{.}0,357\mathrm{.}1,409\mathrm{.}9,367\mathrm{.}3,382\mathrm{.}0],[10,346\mathrm{.}7,452\mathrm{.}9,461\mathrm{.}4,433\mathrm{.}1,410\mathrm{.}6,384\mathrm{.}2,362\mathrm{.}6],[12,407\mathrm{.}4,441\mathrm{.}8,419\mathrm{.}9,410\mathrm{.}7,473\mathrm{.}4,441\mathrm{.}2,465\mathrm{.}8]]$

Does the variation in plate length have any effect on the true average axial stiffness? State and test the relevant hypotheses using analysis of variance $($ANOVA$)$ at a significance level of $0\mathrm{.}01(1\%).$ In addition to your conclusion, are there any recommendations you would make based on the results?