A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records of all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.The 95% confidence interval for π is 0.59 ± 0.07.Interpret this interval.
A) We are 95% confident that 59% of the students are on some sort of financial aid.
B) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
C) 95% of the students get between 52% and 66% of their tuition paid for by financial aid.
D) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.

Question

Quizplus · Accepted Answer

The interval 0.59 ± 0.07 is a confidence interval for the true proportion of all students who receive financial aid. It is not a statement about individual students or how much of their tuition is paid for by financial aid. Option A is incorrect because it is specific to the sample and cannot be generalized to the entire population. Option C is a misinterpretation of the interval, as it suggests that 95% of the students fall within the given range, which is not necessarily true. Option D is partially correct, but it leaves out the important context that the interval is a confidence interval for the true proportion of all students who receive financial aid.

A University Dean Is Interested in Determining the Proportion of Students