In this Excel sheet $($attached below$),$ we have observations of axial$-$stiffness index $($kips$/$in$.)$ for metal plate connected trusses used for roof support lengths $4,6,8,10,$ and $12$ in$.$

Does variation in plate length have any effect on true average axial stiffness? State and test the relevant hypotheses using analysis of variance with

significance level $=0\mathrm{.}01.$

Is it plausible that the variances of the five axial stiffness index distributions are identical? Explain.

Use the Tukey intervals given in the output to determine which means differ, and construct the corresponding underscoring pattern.

stiffness lengths

$309,24$

$409,54$

$3114$

$326,54$

$316,84$

$349,84$

$309,74$

$402,16$

$347,26$

$3616$

$404,56$

$3316$

$348,96$

$381,76$

$392,48$

$366,28$

$3518$

$357,18$

$409,98$

$367,38$

$3828$

$346,710$

$452,910$

$461,410$

$433,110$

$410,610$

$384,210$

$362,610$

$407,412$

$441,812$

$419,912$

$410,712$

$473,412$

$441,212$

$465,812$