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. Suppose we wish to test the null hypothesis that there is no association between year in school and opinion.Under the null hypothesis,what is the expected number of strongly opposed seniors?
A)18
B)25
C)30.5
D)50

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.  Suppose we wish to test the null hypothesis that there is no association between year in school and opinion.Under the null hypothesis,what is the expected number of strongly opposed seniors?
A)18 
B)25 
C)30.5 
D)50

Quizplus · Accepted Answer

To test the null hypothesis, we need to calculate the expected number of strongly opposed seniors assuming no association between year in school and opinion. 
The total number of students in the sample is 4*50 = 200. 
The total number of strongly opposed students is 50+35+20+10 = 115. 
To find the expected number of strongly opposed seniors if there is no association between year in school and opinion, we need to calculate the proportion of strongly opposed students in the sample who are seniors. This is (10/200) = 0.05. 
So the expected number of strongly opposed seniors is 0.05*50 = 2.5*10 = 25. 
Therefore, the best choice is C.

Recent Revenue Shortfalls in a Midwestern State Led to a Reduction