Practise selecting a two-sample z-test when two independent groups provide binary responses and the research question compares their population proportions.
A new anti-spam software program is field-tested on 250 randomly selected spam emails and on 750 randomly selected legitimate emails. The results are summarized in the following table (positive test = program labels email as spam):
\begin{tabular}[t]{|l|l|l|l|}
\hline & Spam & Legitimate & Total \\
\hline Positive
test & 205 & 90 & 295 \\
\hline Negative
test & 45 & 660 & 705 \\
\hline Total & 250 & 750 & 1,000 \\
\hline
\end{tabular}
The software developer claims that the proportion of all spam emails for which the tests are positive equals the proportion of all legitimate emails for which the tests are negative.
Identify the appropriate inference procedure.