Suppose that I completed a test in two different ways. To complete the test, I had to find a p-value by using 'z'

To solve the problem, I use Chi-Square, and the Wilson estimates of the population proportions. Because I approach the question in two different ways, the result of the tests was the same. (Fail to reject Ho for Ha)

z = (P1-hat - P2-hat)/Pooled Standard Errorof the Difference

--> This is what I use to get a z value with the Wilson estimates of the population. proportions

Was the result of the problem a coincidence, or not?

Why or why not?