Chapter 3, Problem 39E

(a)

To determine

To find: the percent of total applicants were admitted.

Answer to Problem 39E

42.6%

Explanation of Solution

Given:

		Males accepted	Females accepted
program	1	511 of 825	89 of 108
	2	352 of 560	17 of 25
	3	137 of 407	132 of 375
	4	22 of 373	24 of 341
	Total	1022 of 2165	262 of 849

Calculation:

Total number of applicant = 2165+849=3014

Applicants admitted = 1022+262=1284

Therefore the percent of total applicants are admitted

  $\begin{array}{l}=\frac{1284}{3014}\times 100\\ =42.6\%\end{array}$

Therefore the required percent is 42.6%

(b)

To determine

To find: that the higher percentage of females and males admitted.

Explanation of Solution

Given:

		Males accepted	Females accepted
program	1	511 of 825	89 of 108
	2	352 of 560	17 of 25
	3	137 of 407	132 of 375
	4	22 of 373	24 of 341
	Total	1022 of 2165	262 of 849

Calculation:

Total number applicants (male) = 2165

Admitted applicants = 1022

  $\begin{array}{l}=\frac{1022}{2165}\times 100\\ =47.2\%\end{array}$

Total number applicants (female) = 849

Admitted applicants = 262

  $\begin{array}{l}=\frac{262}{849}\times 100\\ =30.9\%\end{array}$

Therefore the percentage of male are higher than female admitted.

(c)

To determine

To Explain: the comparison of the males and females admitted in each program.

Explanation of Solution

Given:

		Males accepted	Females accepted
program	1	511 of 825	89 of 108
	2	352 of 560	17 of 25
	3	137 of 407	132 of 375
	4	22 of 373	24 of 341
	Total	1022 of 2165	262 of 849

Calculation:

The percentage of males and females admitted in every program.

	Males accepted (of applicants) %	Females accepted (of applicants) %
Program 1	$\frac{511}{825}\times 100=61.9\%$	$\frac{89}{108}\times 100=82.4\%$
Program 2	$\frac{352}{560}\times 100=62.9\%$	$\frac{17}{25}\times 100=68.0\%$
Program 3	$\frac{137}{407}\times 100=33.7\%$	$\frac{132}{375}\times 100=35.2\%$
Program 4	$\frac{22}{373}\times 100=5.9\%$	$\frac{24}{341}\times 100=7.0\%$

It is observed that males have lower percentage of admittance in every program in comparison to females.

(d)

To determine

To Explain: the comparison for the consideration to be the most valid.

Explanation of Solution

The comparisons in part (c) represent that males have a lower admittance rate in every program, even though the overall rate represent males with a higher rate of admittance. This is an example of Simpson’s paradox. Part (c) is the most valid.