To estimate how many of the 800 students own cats using the information provided, we can set up a proportion based on the sample of 50 students.
From the information given:
- Number of students surveyed (sample): \( 50 \)
- Number of students in the sample who own cats: \( 4 \)
- Total number of students: \( 800 \)
The proportion is set up as follows:
\[ \frac{\text{Number of students who own cats in sample}}{\text{Total number of students in sample}} = \frac{\text{Estimated number of students who own cats in total}}{\text{Total number of students}} \]
Substituting the known values:
\[ \frac{4}{50} = \frac{x}{800} \]
Now, we can solve for \( x \):
- Cross multiply to get rid of the fraction:
\[ 4 \times 800 = 50 \times x \]
- Calculate \( 4 \times 800 \):
\[ 3200 = 50x \]
- Now, divide both sides by 50:
\[ x = \frac{3200}{50} = 64 \]
Thus, the estimated number of students who own cats among the 800 students is \( \boxed{64} \).