What departments are the hardest to be admitted into?

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$-$

$6$

$.$

$$What departments are the easiest to be admitted into?

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$-$

$7$

$.$

$$What departments are the males applying to the most?

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$8$

$.$

$$What departments are the females applying to the least?

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$9$

$.$

$$Which of the following are true:

Females have a higher admittance rate overall and within each department.

Females have a higher admittance rate overall but within each department males often have a higher admittance rate.

This is an example of Simpson's Paradox

Males have a higher admittance rate overall but within departments females often have a higher admittance rate.

Males have a higher admittance rate overall and within each department.Contingency Tables

$\backslash$table$[[,,$Admitted,$],[$Department$,$Gender,No$,$Yes,Total$],[$Chemistry$,$Female,$8,17,25],[,$Male,$210,350,560],[,$Total,$218,367,585],[$History$,$Female,$316,25,341],[,$Male,$349,24,373],[,$Total,$665,49,714],[$Law$,$Female,$299,94,393],[,$Male,$138,53,191],[,$Total,$437,147,584],[$Math$,$Female,$19,89,108],[,$Male,$320,505,825],[,$Total,$339,594,933],[$Total$,$Female,$642,225,867],[,$Male,$1017,932,1949],[,$Total,$1659,1157,2816]]$