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 Role - Total
Received Math Class Requested 125 215 340
Didn't 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

The probability of an honor roll student getting their requested math class is approximately 60.98%, while for non-honor roll students it is approximately 72.88%. Non-honor roll students have a higher probability of getting their requested class, which suggests no unfair advantage for honor roll students.

Step-by-step explanation:

To determine if all students have an equal opportunity to get into the math class they requested, we need to use the information provided in the contingency table. Specifically, we will calculate the probability of an honor roll student and a non-honor roll student getting the math class they requested and compare these probabilities.

From the table, there are a total of 205 honor roll students. Out of these, 125 received the math class they requested. So, the probability (P) of an honor roll student getting the class they requested is P(Honor Roll Gets Class) = 125/205.

There are 295 non-honor roll students, and 215 of them received the math class they requested. The probability of a non-honor roll student getting the class they requested is P(Non-Honor Roll Gets Class) = 215/295.

Let's calculate these probabilities:

• P(Honor Roll Gets Class) = 125/205 ≈ 0.6098 or 60.98%
• P(Non-Honor Roll Gets Class) = 215/295 ≈ 0.7288 or 72.88%

Based on these probabilities, non-honor roll students have a higher probability of getting their requested math class than honor roll students. Hence, there might be some evidence that contradicts Shelly's belief of an unfair advantage for honor roll students in this scenario. However, further statistical analysis, like a chi-square test of independence, might be needed to make a conclusive statement.