Step 1 :Given that the number of respondents who said 'yes' is $x = 564$ and the total number of respondents is $n = 1094$.
Step 2 :The best point estimate of the population proportion $p$ is given by the formula $p = \frac{x}{n}$.
Step 3 :Substitute $x = 564$ and $n = 1094$ into the formula to get $p = \frac{564}{1094}$.
Step 4 :Simplify the fraction to get $p = 0.5155393053016454$.
Step 5 :Round the result to four decimal places to get $p = 0.5155$.
Step 6 :\(\boxed{0.5155}\) is the best point estimate of the population proportion $p$.