In a high school class with senior students, $3$ different Turkish teaching techniques were applied to $3$ groups of students and it was aimed to determine whether these different techniques had an effect on the grades received. For this purpose, $4$ students from the first group, $5$ students from the second group and $6$ students from the third group were randomly selected and the grades they received out of $100$ from the relevant course are given in the following table. What is the test statistic value used to test whether there is a significant difference between teaching techniques at the $5\%$ significance level?

Bir lisede son s$$n$$f $$rencilerinin bulundu$$u bir s$$n$$fta$,3$renci grubuna $3$ farkl$$ T$$rk$$e $$retim tekni$$i uygulanm$$ ve bu farkl tekniklerin al$$nan notlar $$zerinde bir etkisi olup olmad$$ belirlenmek istenmi$$tir$.$ Bu ama$$la birinci gruptan $4,$ ikinci gruptan $5$ ve $$nc$$ gruptan $6$renci rassal olarak se$$ilmi$$ ve ilgili dersten $100$zerinden ald$$klar$$ notlar izleyen tabloda verilmi$$tir$.$retim teknikleri aras$$nda anlaml fark olup olmad$$n$$n $\%5$ anlam d$$zeyinde test edilmesinde kullan$$lan test istatisti$$i de$$eri ka$$t$$r$?$

$\backslash$table$[[$Group $1,$Group $2,$Group$3],[10,30,50],[20,60,70],[40,60,80],[50,70,90],[,80,90],[,,100]]$

$11$

$9$

$6,5$

$1,25$

$3,88$

Bo$$ birak