A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to ensure each college is represented fairly.The below table shows the observed number of students who participate in the poll from each college and the actual proportion of students in each college. Which of the following is the value of the goodness-of-fit test statistic?
A) 3.08
B) 15.09
C) 15.64
D) 16.75

Question

A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to ensure each college is represented fairly.The below table shows the observed number of students who participate in the poll from each college and the actual proportion of students in each college.  Which of the following is the value of the goodness-of-fit test statistic?
A) 3.08 
B) 15.09 
C) 15.64 
D) 16.75

Quizplus · Accepted Answer

The goodness-of-fit test statistic is calculated by summing the squared difference between the observed and expected values of each category divided by the expected value for each category. The expected value for each category is the total number of students who participated in the poll multiplied by the proportion of students in each college. Using the table provided, we can calculate the expected value and the squared difference for each college:

College A: Expected = 1200*0.25=300, (119-300)^2/300 = 39.07
College B: Expected = 1200*0.2=240, (262-240)^2/240 = 1.47
College C: Expected = 1200*0.15=180, (225-180)^2/180 = 12.5
College D: Expected = 1200*0.2=240, (223-240)^2/240 = 1.79
College E: Expected = 1200*0.1=120, (103-120)^2/120 = 2.25
College F: Expected = 1200*0.1=120, (71-120)^2/120 = 16.25

Summing up these values gives us a test statistic of 15.64, which is closest to option C.

A University Has Six Colleges and Takes a Poll to Gauge