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AP Statistics 3.13 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions

Practise calculating two-proportion z-statistics and p-values by pooling under the null, respecting the alternative direction, and using normal or simulated tails.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Pool successes across both groups under H0 to compute the two-proportion z-test standard error.
  • Use the alternative direction to choose one tail or double the corresponding tail probability.
  • Estimate a randomization p-value by counting simulated differences at least as extreme as observed.

AP Statistics 3.13 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions question 1

[Maximum number: 5]

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.

Figure for Question AP Statistics 3.13 A Calculate an Appropriate Test Statistic and P Value for Testing a Hypothesis for the Difference Between Two Questions question 1 — AP Statistics

Complete the inference procedure, including calculations.

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