Chapter 15, Problem 31E

To determine

To Explain: that party affiliation independent of the respondents’ sex.

Explanation of Solution

Given:

	Democrat	Republican	Independent
Male	36	45	24
Female	48	33	16

Calculation:

Let D = Respondent is affiliated to Democrat

R = Respondent is affiliated to Republic

I = Respondent is affiliated to Independent

M = Respondent is male

F = Respondent is female

Suppose,

  $\begin{array}{c}P\left(D|M\right)=\frac{P\left(D\cap M\right)}{P\left(M\right)}\\ P\left(D\cap M\right)=\frac{36}{202}\\ P\left(M\right)=\frac{105}{202}\end{array}$

  $\begin{array}{c}P\left(D|M\right)=\frac{\frac{36}{202}}{\frac{105}{202}}\\ =\frac{36}{105}\\ =34.29\\ P\left(D\right)=\frac{84}{202}\\ =0.4158\end{array}$

Although $P\left(D|M\right)\ne P\left(D\right)$ party affiliation is not independent of the respondents sex