A survey of footwear preferences of a random sample of $100$ undergraduate students from a large university resulted in the following data:

$\backslash$table$[[$Footwear Preference,Total$],[,$Boots,Shoes,Sandals$],[$Male$,8,18,15,],[$Female$,13,39,7,],[$Total$,,,,]]$

We are interested in carrying out a hypothesis test to determine whether gender and footwear preference are related.

a$.$ What are the $H_0$ and $H_a$ be for this test?

b$.$ If $H_0$ is true, what would be the expected count be for female students who prefer shoes?

c$.$ What are the degrees of freedom for this test?

d$.$ What would be the p$-$value for the Chi$-$Square $=8\mathrm{.}884?$

e$.$ What conclusion can be reached, using $=\mathrm{.}05?$