The National Academy of Science reported that \( 33 \% \) of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer \( 33 \% \). He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer \( 33 \% \) ? Use a 0.01 level of significance.

To determine whether there is sufficient evidence to support the claim that the percentage of articles published by US authors is no longer \( 33\% \), we'll conduct a hypothesis test with the following steps: 1. **State Hypotheses**: - Null hypothesis (\( H_0 \)): \( p = 0.33 \) (the true proportion of articles by US authors is \( 33\% \)) - Alternative hypothesis (\( H_a \)): \( p \neq 0.33 \) (the true proportion of articles by US authors is not \( 33\% \)) 2. **Sample Proportion**: - Sample size (\( n \)) = 280 - Number of articles by US authors = 108 - Sample proportion (\( \hat{p} \)) = \( \frac{108}{280} \approx 0.3857 \) 3. **Standard Deviation of the Sampling Distribution**: - Standard deviation (\( \sigma_{\hat{p}} \)) when \( p = 0.33 \): \[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.33 \times 0.67}{280}} \approx 0.0295 \] 4. **Calculate the Z-Score**: \[ Z = \frac{\hat{p} - p}{\sigma_{\hat{p}}} = \frac{0.3857 - 0.33}{0.0295} \approx 1.885 \] 5. **Critical Value**: At a significance level (\( \alpha \)) of \( 0.01 \) for a two-tailed test, the critical z-values are approximately \( \pm2.576 \). 6. **Comparison**: Since \( 1.885 \) does not exceed \( 2.576 \) (in either direction), we do not reject the null hypothesis. ### Conclusion: At the \( 0.01 \) level of significance, there is not enough evidence to support the mathematics chairperson's claim that the proportion of articles published by US authors is no longer \( 33\% \). --- Historical Background: Mathematics publication in the United States has seen significant trends over the decades, often reflecting not just internal academic dynamics, but also broader cultural and political movements. The post-World War II era marked an explosion in mathematical research, with American mathematicians gaining prominence as top contributors on the global stage, further shaping the landscape of mathematical publications. Real-World Application: Understanding this percentage can help institutions devise strategies to encourage more diversity in research authorship. If certain demographics are underrepresented, universities can work on creating mentorship programs or funding opportunities aimed explicitly at fostering a more inclusive research environment, ultimately enhancing the richness of academic discourse and innovation.