Certainly! Let's solve this step-by-step to determine the proportion of pet owners who have either a cat or a dog in the given survey sample.
1. Flatten the Sample Data:
First, we take the provided sequence of random digits:
```
08979, 61956, 77989, 04853, 28580, 80896
```
Flatten them into a single string:
```
089796195677989048532858080896
```
2. Total Number of Digits:
We count the total number of digits in the string. In this case, there are 30 digits.
3. Identify Even Digits:
Count the number of even digits (since each even digit represents a cat or dog owner):
```
0, 8, 9, 7, 9, 6, 1, 9, 5, 6, 7, 7, 9, 8, 9, 0, 4, 8, 5, 3, 2, 8, 5, 8, 0, 8, 9, 6
```
The even digits among these are:
```
0, 8, 6, 6, 8, 0, 4, 8, 2, 8, 8, 0, 8, 6
```
Counting these gives us 16 even digits.
4. Calculate the Proportion:
Finally, we find the proportion of even digits to the total number of digits:
[tex]\[
\frac{\text{Number of even digits}}{\text{Total number of digits}} = \frac{16}{30} \approx 0.5333333333
\][/tex]
Given these calculations, the proportion of respondents who own either a cat or a dog is approximately 0.53.
Thus, the best estimate of the proportion of responses in a sample who own either a cat or a dog is:
[tex]\[
\boxed{0.53}
\][/tex]
