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 1253 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?" 55.9% said they felt burdened.

_______, _______

(b) "If you could begin again, taking into account your current experience, what would you borrow?" 54.7% 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." 33.2% disagreed.

_______, _______

(d) "Making loan payments is unpleasant but I know that the benefits of education loans are worth it." 59.9% agreed.

_______, _______

(e) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for career opportunities." 58.2% agreed.

_______, _______

(f) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for personal growth." 71.3% agreed.

_______, _______

Conclusion

While many feel that loans are a burden and wish they had borrowed less, a majority are satisfied with their education.

While a minority feel that loans are a burden and wish they had borrowed more, a minority are satisfied with their education.     

While many feel that loans are a burden and wish they had borrowed less, a minority are satisfied with their education.

While a minority feel that loans are a burden and wish they had borrowed more, a majority are satisfied with their education.

Answer 1

a)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.559 - (1.9599639861)(0.014026511211266204) = 0.5315085432

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.559 + (1.9599639861)(0.014026511211266204) = 0.5864914568

Confidence Interval = (0.532, 0.586)

b)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.547 - (1.9599639861)(0.014062651967787543) = 0.5194377086

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.547 + (1.9599639861)(0.014062651967787543) = 0.5745622914

Confidence Interval = (0.519, 0.575)

c)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.332 - (1.9599639861)(0.013303984725525476) = 0.3059246691

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.332 + (1.9599639861)(0.013303984725525476) = 0.3580753309

Confidence Interval = (0.306, 0.358)

d)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.599 - (1.9599639861)(0.013845545208006196) = 0.57186323

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.599 + (1.9599639861)(0.013845545208006196) = 0.62613677

Confidence Interval = (0.572, 0.626)

e)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.582 - (1.9599639861)(0.013933945184756961) = 0.5546899693

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.582 + (1.9599639861)(0.013933945184756961) = 0.6093100307

Confidence Interval = (0.555, 0.609)

f)

z_α/2 = 1.9599639861

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.713 - (1.9599639861)(0.012779391580275298) = 0.6879528527

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.713 + (1.9599639861)(0.012779391580275298) = 0.7380471473

Confidence Interval = (0.688, 0.738)

g)

While many feel that loans are a burden and wish they had borrowed less, a majority are satisfied with their education.