The Princeton Review 2016 College Hopes and Worries Survey Report (princetonreview.com/cms -content/final_cohowo2016survrpt.pdf, retrieved May 6, 2017) reported that 31% of students applying to college wanted to attend a college that was within 250 miles of their home and that 51% of parents of students applying to college wanted their child to attend a college that was within 250 miles from home. Suppose that the reported percentages were based on random samples of 8347 students applying to college and of 2087 parents of students applying to college.

a. Construct and interpret a 90% confidence interval for the proportion of students applying to college who want to attend a college within 250 miles of their home.

b. Construct and interpret a 90% confidence interval for the proportion of parents of students applying to college who want their child to attend a college within 250 miles from home.

c. Explain why the two 90% confidence intervals are not the same width.