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A study reports that about half of pet owners have either a dog or a cat. The other half of pet owners have birds, reptiles, or other animals. To find out if this applies in its area, an animal shelter surveys a random sample of 30 pet owners. Nineteen of them say they own either a cat or a dog.

Let even digits represent owning a cat or a dog and odd digits represent owning some other type of animal.

\begin{tabular}{|l|l|l|l|l|l|}
\hline 08979 & 61956 & 77989 & 04853 & 28580 & 80896 \\
\hline
\end{tabular}

Using the line of random numbers, what is the best estimate of the proportion of responses in a sample who own either a cat or a dog?

A. 0.47
B. 0.50
C. 0.53
D. 0.63



Answer :

GinnyAnswer
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]

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