Josh believes the Spanish club students at his school have an unfair advantage in being assigned to the Spanish class they request. He asked 500 students at his school the following questions: "Are you in the Spanish club?" and "Did you get the Spanish class you requested?" The results are shown in the table below:
Josh determine if all students at his school have an equal opportunity to get the Spanish class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Spanish Club and Did not Receive Spanish Class Requested - 265
Not in Spanish Club and Receive Spanish Class Requested - 100
Total: 365
Did not get Spanish Class Requested and Spanish Club- 70
Did not get Spanish Class Requested and Not in Spanish Club- 65
Total: 135
Total Spanish Club: 335
Total Not in Spanish Club: 165
Overall Total: 500

You can calculate the following probabilities:
1. Given that a sampled student is in the Spanish Club, what is the probability they got the Spanish class they requested?
2. Given that a sampled student is not in the Spanish Club, what is the probability they got the Spanish class they requested? If there is a significant difference between the two probabilities, it indicates there is a bias in the selection procedure.
Given that, a sampled student is in the Spanish Club, the probability they got the Spanish class they requested is given by 265/335. Given that, a sampled student is not in the Spanish Club, the probability they got the Spanish class they requested is given by 100/165.
If a student is at the Spanish club, the probability they got the Spanish class they requested is 265/335 = 0.79. If a student is not in the Spanish club, the probability they got the Spanish class they requested is 100/165 = 0.61.
Based on the calculation, all students do not have an equal chance of getting into the Spanish class that they requested.


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