Use the table to answer the question.

Question

Prefer Dogs Prefer Cats Total
Backyard 15 7 22
No Backyard 6 17 23
Total 21 24 45
A researcher collected data on a group of students in an after-school program. She asked them whether they preferred dogs or cats, and whether they did or did not have a backyard at home. She compiled the data in a two-way table. Interpret the table to identify the conditional relative frequency of students who prefer dogs, given they have a backyard.

(1 point)
Responses

63%
63% - no response given

32%
32% - no response given

68%
68% - no response given

71%

Answer 1

To find the conditional relative frequency of students who prefer dogs given they have a backyard, we need to use the relevant data from the table.

1. Identify the number of students who prefer dogs and have a backyard:
   From the table, this number is 15.

2. Identify the total number of students who have a backyard:
   The total number of students who have a backyard is 22 (15 who prefer dogs + 7 who prefer cats).

3. Calculate the conditional relative frequency:
   The formula for conditional relative frequency is:
   \[ \text{Relative frequency} = \frac{\text{Number who prefer dogs and have a backyard}}{\text{Total with backyard}} \times 100 \]
   Plugging in the values:
   \[ \text{Relative frequency} = \frac{15}{22} \times 100 \approx 68.18% \]

Thus, rounding to the nearest whole number, the conditional relative frequency of students who prefer dogs given they have a backyard is 68%.

So the correct response is 68% - no response given.