A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 1. ± 0.07. Interpret this interval.
A) 95% of the students get between 52% and 66% of their tuition paid for by 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) We are 95% confident that 59% of the students are on some sort of 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 confidence interval provides a range of values in which the true proportion of all students receiving financial aid is likely to fall. We can say with 95% confidence that the true proportion lies between 0.52 and 0.66. Choice A is incorrect because it refers to individual students, not the overall proportion. Choice C is incorrect because it assumes a specific value for the proportion. Choice D is partly correct but does not provide the full interpretation of the confidence interval.

A University Dean Is Interested in Determining the Proportion of Students