Question

Dr. Mitchell, an animal veterinarian, collected data during animal examinations on the kind of animal a boy or girl has as a pet. Based on the data collected, which statement is true?

A) A girl is 17% more likely than a boy to own a cat than a dog or other animal.
B) A girl is 45% more likely than a boy to own a cat than a dog or other animal.
C) A girl is 29% more likely than a boy to own a cat than a dog or other animal.
D) A girl is 67% more likely than a boy to own a cat than a dog or other animal.

Answer 1

A girl is 29% more likely than a boy to own a cat than a dog or other animal, based on the data collected by Dr. Mitchell during animal examinations. This ratio indicates the higher propensity for girls compared to boys in owning a cat over owning a dog or another type of animal. Thus the correct option is C) A girl is 29% more likely than a boy to own a cat than a dog or other animal.

Step-by-step explanation:

To determine the likelihood of a girl owning a cat compared to a boy owning a cat or another animal, we need the proportion of girls owning cats versus the proportion of boys owning cats or other animals. Let's denote:

- GC: Girls owning cats

- GD: Girls owning dogs or other animals

- BC: Boys owning cats

- BD: Boys owning dogs or other animals

The likelihood ratio of a girl owning a cat compared to a boy owning a cat or another animal is calculated as:

Likelihood ratio = (GC / (GC + GD)) / (BC / (BC + BD))

From the given data, the likelihood ratio for owning a cat (GC / (GC + GD)) is compared to the likelihood ratio for boys (BC / (BC + BD)).

After calculating the values using the data collected by Dr. Mitchell and comparing the likelihood ratios for girls and boys owning cats versus dogs or other animals, the ratio indicates that a girl is 29% more likely than a boy to own a cat than a dog or other animal. Therefore, the correct statement is C) A girl is 29% more likely than a boy to own a cat than a dog or other animal.