Example 26

EXAMPLE 26 Determining independence using the alternative method

We return to the direct mail marketing data from Example 19, reproduced here in Table 23. Use the alternative method for determining independence to determine whether the following two events are independent:

$R : Responded to direct mail marketing campaign.$
$C : Has a credit card on file.$

Table 5.56: Table 23 Credit card status and marketing response

Response	Credit card on file?
Response	No	Yes	Total
Did not respond	161	79	240
Did respond	17	31	48
Total	178	110	288

Table 5.56: Source: Daniel Larose and Chantal Larose, Data Mining and Predictive Analytics (Wiley Interscience, 2015).

Solution

Using Table 23, we may find the following probabilities:

$\begin{matrix} P (R) = \frac{48}{288} P (C) = \frac{110}{288} P (R a n d C) = \frac{31}{288} \approx 0.1076 \\ P (R) \cdot P (C) = \frac{48}{288} \cdot \frac{110}{288} \approx 0.0637 \end{matrix}$

Because $0.0637 \neq 0.1076$ , we have $P (R) \cdot P (C) \neq P (R and C)$ ; therefore, $R$ and $C$ are dependent.

NOW YOU CAN DO

Exercises 79–84.