Question

Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:


Honor roll Not on honor roll Total
Received math class requested 125 215 340
Did not get math class requested 80 80 160
Total 205 295 500


Help Shelly determine if all students at her school have an equal opportunity to get into the math class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.

Answer 1

on a very basic level, you'd want to calculate the proportion of honor roll students who got the class they wanted vs. non-honor roll students who got the class they wanted, then compare the two proportions

if this is an AP/college-level course, you'd also want to do a z-test for two sample proportions to see whether the difference is significant or not

https://online.stat.psu.edu/stat800/lesson/5/5.5