James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his 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.

Question

anonymous · Answer

Honor roll Not on honor roll Total
 Received math class requested 315 64 379
 Did not get math class requested 41 80 121
 Total 356 144 500 

 Help James determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.

jtvatsim · Answer

We might try to do this by just calculating the percent.

Unless, has your class covered the chi^2 test?

anonymous · Answer

No we didn't

anonymous · Answer

@jtvatsim

jtvatsim · Answer

OK, then we should just use percents. Let's find 1) the percent of honors students who got the class they requested and 2) the percent of not honors students who got the class they requested.

jtvatsim · Answer

We will then compare the percents to see if one group gets the class they requested more often (e.g., does one group have a bigger percentage than the other).

jtvatsim · Answer

To find the percent of honors students that got the class they requested, we first need to know:
1) how many honors students are there?
2) how many got the class they requested? 

What do you think the answers to these questions are?

anonymous · Answer

There are 379 honors students and 315 got the class they requested

jtvatsim · Answer

Ah! But that's the trick, the 379 is the total of all students who received the class they wanted. We need the "other total" :)

anonymous · Answer

Oh so 356

jtvatsim · Answer

Yes, and 315 got the class they wanted like you said before. :)

jtvatsim · Answer

Great! Now we can calculate the percent: 315/356 = about 0.88 or 88%. That's really good odds of getting the class you want!

jtvatsim · Answer

One more piece to go, but does this make sense so far?

anonymous · Answer

Yes it does :) next we would take the number of students who were not in honor roll and got the class they requested, correct?

jtvatsim · Answer

Yes that is right. Let's do it.

anonymous · Answer

There are 144 students who are not in honor roll and 64 got the class they requested. So it would be 64/144= about .044 or 44%

jtvatsim · Answer

Excellent.

jtvatsim · Answer

Hmm... so that's a pretty big difference.

jtvatsim · Answer

For honors students, 88% of them will get the class they requested... but for non honors students it's worse than flipping a coin, 44%.

jtvatsim · Answer

To wrap it up and answer the questions concern to explain "fairness," we are basically saying that "fairness" would be if both percents were equal (or at least close to equal). Since they aren't we would say that the situation is "unfair."

anonymous · Answer

Alright I understand it now :) thank you so much

jtvatsim · Answer

You are welcome! Good luck!