The National Student Loan Survey asked the student loan borrowers in their sampl

Question

The National Student Loan Survey asked the student loan borrowers in their sample about attitudes toward debt. Below are some of the questions they asked, with the percent who responded in a particular way. Assume that the sample size is 1266 for all these questions. Compute a 95% confidence interval for each of the questions, and write a short report about what student loan borrowers think about their debt. (Round your answers to three decimal places.)

(a) "To what extent do you feel burdened by your student loan payments?" 56.3% said they felt burdened.

  ,

(b) "If you could begin again, taking into account your current experience, what would you borrow?" 55% said they would borrow less.

  ,

(c) "Since leaving school, my education loans have not caused me more financial hardship than I had anticipated at the time I took out the loans." 33.8% disagreed.

  ,

(d) "Making loan payments is unpleasant but I know that the benefits of education loans are worth it." 58.6% agreed.

  ,

(e) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for career opportunities." 58.7% agreed.

  ,

(f) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for personal growth." 69.3% agreed.

  ,

Explanation / Answer

n=1266

solutiona:

p^=56.3%=0.563

z alpha/2 for 95%=1.96

95% confidence interval forpopulation proportion of students who feel burdened by student loan payments

are

p^-zcritsqrt(p^(1-p^)/n),p^+zcritsqrt(p^(1-p^)/n)

0.563-1.96 sqrt(0.563(1-0.563)/1266),0.563+1.96 sqrt(0.563(1-0.563)/1266)

0.536,0.590

lower limit=0.536

upper limit=0.590

(b) "If you could begin again, taking into account your current experience, what would you borrow?" 55% said they would borrow less.

95% confidence interval forpopulation proportion of students who feel that they would borrwo less is

0.55-1.96 sqrt(0.55(1-0.55)/1266),0.55+1.96 sqrt(0.55(1-0.55)/1266)

0.523,0.577

lower limit=52.3%

upper limit=57.7%

Solutionc:

95% confidence interval forpopulation proportion of studentsis

0.338-1.96 sqrt(0.338(1-0.338)/1266),0.338+1.96 sqrt(0.338(1-0.338)/1266)

0.311, 0.364

lower limit=0.311

upper limit 0.364

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