Question

the two - way table given shows the results from a survey of pet owners.

	owns a cat	does not own a cat	total
does not own a dog	45	15	60
total	171	69	240

does the data show an association between owning a dog and owning a cat?

• there is a strong, positive association.
• there is a strong, negative association.
• there is a weak, negative association.
• there is a weak, positive association.

Explanation:

Step1: Calculate conditional probabilities

For those who own a dog, the proportion who own a cat: $\frac{126}{180} = 0.7$.
For those who do not own a dog, the proportion who own a cat: $\frac{45}{60} = 0.75$.

Step2: Analyze the association

The two proportions (0.7 and 0.75) are close, indicating a weak association. Since both proportions are relatively high (owning a cat is more common in both groups), and the difference is small, the association is weak and positive (as both proportions are high, suggesting a tendency for those who own a dog to also own a cat, though weakly).

Answer:

There is a weak, positive association.