Question

According to the U.S. Department of Education, 10.8% of all borrowers in the federal student loan programs’ fiscal year 2015 cohort defaulted on their loan. Consider a SRS of 300 federal student loan borrowers in the most recent cohort. Let’s say your SRS results in 15 borrowers who defaulted. Calculate a z-score for this sample result when the population default rate is
a. 0.01.
b. 0.02.
c. 0.04.
d. 0.06.
e. 0.08.
f. 0.10.
g. A population default rate is considered reasonable if it results in |?| < 2 for the sample statistic. Using this
criterion, which population default rates (a – f) are reasonable based on the data?

Answer 1

n = SRS result in 15 borrowers = 15

p = population default rate

The population default rates are given in parts a to f

The formula of z score for the sample proportion that is sample default rate is,

a. p = 0.01

The z score is,

b. p = 0.02

c. p = 0.04

d. p = 0.06

e. p = 0.08

f. p = 0.10

g. |3.81| = 3.81, |2.423| = 2.43, |1.34| = 1.34, |0.78| = 0.78, |0.40| = 0.40, |10| = 0.10

z scores for parts c, d, e and f are < 2

The population rates 0.04, 0.06, 0.08 and 0.10 are considered as reasonable based on the data.