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### Kurs: Statystyka - program rozszerzony>Rozdział 12

Lekcja 2: Testowanie różnicy między dwiema proporcjami

# Wyciąganie wniosków na temat różnicy proporcji

A university offers a certain course that students can take in-person or in an online setting. Teachers of the course were curious if there was a difference in the passing rate between the two settings. Data from a recent semester showed that $80\mathrm{%}$ of students passed the in-person setting, and $75\mathrm{%}$ of students passed the online setting. They were willing to treat these as representative samples of all students who may take each setting of the course.
The teachers used those results to make a $95\mathrm{%}$ confidence interval to estimate the difference between the proportion of students who pass in each setting of the course $\left({p}_{\text{in-person}}-{p}_{\text{online}}\right)$. The resulting interval was approximately $\left(-0.04,0.14\right)$. They want to use this interval to test ${H}_{0}:{p}_{\text{in-person}}={p}_{\text{online}}$ versus ${H}_{\text{a}}:{p}_{\text{in-person}}\ne {p}_{\text{online}}$. Assume that all conditions for inference have been met.
Based on the interval, what do we know about the corresponding P-value and conclusion at the $\alpha =0.05$ level of significance?