Question

George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown in the table below:
Art Club Not in Art Club Total
Received art class requested 100 265 365
Did not get art class requested 65 70 135
Total 165 335 500


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

Answer 1

Answer:

  class assignment seems to discriminate against Art Club members

Step-by-step explanation:

The probability of getting the requested assignment given that the student was in Art Club was ...

  P(got class | art club) = P(got class & art club)/P(art club)

  P(got class | art club) = (100/500)/(165/500) ≈ 60.6%

__

  P(got class | not club) = P(got class & not club)/P(not club)

  P(got class | not club) = (265/500)/(335/500) ≈ 79.1%

It looks like George's theory may be incorrect, as a significantly greater percentage of non-club students got their requested class than did club students. The class assignment process and art club membership are not independent, suggesting an unfair disadvantage for club students.