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

We can use the chi-squared goodness-of-fit test to determine if the observed counts of students in each college who participated in the poll differs significantly from the expected counts based on the actual proportions of students in each college. Using the formula chi-squared = Σ (observed - expected)^2 / expected, we can calculate the chi-squared value to be 15.64. Therefore, the answer is C.

A University Has Six Colleges and Takes a Poll to Gauge