Step 1 :The hypothesized population proportion for this test is given as the proportion of students in the element schools who were classified as only children. This is the proportion we are testing against, so it is our hypothesized population proportion.
Step 2 :From the problem statement, we know that 32% of the students in the element schools were classified as only children. Therefore, the hypothesized population proportion for this test is \(p=0.32\).
Step 3 :\(\boxed{p=0.32}\)