Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education.To offset the reduction,the largest state university proposed a 25% tuition increase.It was determined that such an increase was needed to simply compensate for the lost support from the state.Random samples of 50 freshmen,50 sophomores,50 juniors,and 50 seniors from the university were asked whether or not they were strongly opposed to the increase,given that it was the minimum increase necessary to maintain the university's budget at current levels.The results are given in the following table. To compare the four classes (years in school)with respect to their opinions regarding the proposed tuition increase,which distribution should we calculate?
A)The joint distribution of year in school and opinion
B)The marginal distribution of opinion
C)The conditional distribution of year in school given opinion
D)The conditional distribution of opinion given year in school

Question

Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education.To offset the reduction,the largest state university proposed a 25% tuition increase.It was determined that such an increase was needed to simply compensate for the lost support from the state.Random samples of 50 freshmen,50 sophomores,50 juniors,and 50 seniors from the university were asked whether or not they were strongly opposed to the increase,given that it was the minimum increase necessary to maintain the university's budget at current levels.The results are given in the following table.  To compare the four classes (years in school)with respect to their opinions regarding the proposed tuition increase,which distribution should we calculate?
A)The joint distribution of year in school and opinion 
B)The marginal distribution of opinion 
C)The conditional distribution of year in school given opinion 
D)The conditional distribution of opinion given year in school

Quizplus · Accepted Answer

To compare the opinions of each year in school, we need to calculate the conditional distribution of opinion given year in school (i.e., given the specific demographic). This will allow us to see if there are any significant differences in opinion among the different years in school. The joint distribution of year in school and opinion would provide information about the overall distribution, but wouldn't allow us to compare the different years in school. The marginal distribution of opinion would only provide information about the overall percentage of students opposed to the increase, without taking into account any differences among the different years in school.

Recent Revenue Shortfalls in a Midwestern State Led to a Reduction