Thanks for the example Rick. This one can throw you if you don't dig into it a bit. A lot of the examples will use the option: testp=(30 12 30 25 3). This does something different. When you're first learning chi-squared a lot of the text will start with an example where the intended proportions are stated, and you are just looking for conformity to those proportions. The testp option is good for that. In real life though, you are often wanting to compare two data groups, both randomly sampled from the environment and you want to ask how likely it is that they are drawn from the same population with respect to proportions. That's a different question because both are random draws and neither is locked down. That means there are two sources of uncertainty, not one. Your example shows how to estimate Ho for p_1 = p_2 in that situation.

Thanks.