A researcher wants to know if the clothes a woman wears is a factor in her GPA. The table below shows data that was collected from a survey.

$\backslash$table$[[$Shorts$,$Dress,Jeans,Skirt$],[3\mathrm{.}3,2\mathrm{.}2,3\mathrm{.}9,1\mathrm{.}8],[3\mathrm{.}9,3\mathrm{.}1,3,2\mathrm{.}6],[3\mathrm{.}1,1\mathrm{.}8,3\mathrm{.}8,3\mathrm{.}4],[3\mathrm{.}7,2\mathrm{.}5,3\mathrm{.}9,3\mathrm{.}8],[3\mathrm{.}4,3\mathrm{.}7,3,1\mathrm{.}8],[4,2,2\mathrm{.}3,1\mathrm{.}9],[2\mathrm{.}8,2\mathrm{.}4,3\mathrm{.}6,2\mathrm{.}5],[3\mathrm{.}9,2\mathrm{.}6,,2\mathrm{.}4],[2,,,]]$

and the data was collected independently and randomly. Use a level of significance of $=0\mathrm{.}1.$

$H_0$:${}_1={}_2={}_3={}_4$

$H_1$ : At least two of the means differ from each other.

For this study, we should use Select an answer

The test$-$statistic for this data $=($Please show your answer to $3$ decimal places.$)$

The $p-$value for this sample $=($Please show your answer to $4$ decimal places.$)$

The $p-$value is Select an answer $$

Base on this, we should hypothesis

As such, the final conclusion is that...

There is insufficient evidence to support the claim that the clothes a woman wears is a factor in GPA.

There is sufficient evidence to support the claim that the clothes a woman wears is a factor in GPA.