Points$]$

USEESTAT$412.$E$\mathrm{.}029.$

point can be made with similar, hypothetical numbers. For simplicity, we will assume there are only two graduate programs. The figures for acceptance to each program are shown in the table.

An Example of Simpson's Paradox

$($a$)$ Combine the data for the two programs into one aggregate table. What percentage of all men who applied were admitted? What percentage of all women who applied were admitted?

Which sex was more successful?

men

women

$($b$)$ What percentage of the men who applied did Program A admit? What percentage of the women who applied did Program A admit? $($Round your answer to one decimal place.$)$

men

women

$\%$

Which

men

women

What percentage of the men who applied did Program B admit? What percentage of the women who applied did Program B admit? $($Round your answer to one decimal place.$)$

Which sex was more successful in getting admitted to Program B$?$

men

women

$($c$)$ Explain how this problem is an example of Simpson's Paradox. $($Hint: Which program was easier to get admitted to overall? Which program interested men more? Which program interested women more?$)$