Question

Student loan default rate. The national student loan default rate has fluctuated over the past several years. Recently (October 2015) the Department of Education reported the default rate (i.e., the proportion of college students who default on their loans) at 0.12. Set up the null and alternative hypotheses if you want to determine if the student loan default rate this year is less than 0.12.
The testing claimed by the national student loan default rate is the test for a specified proportion.

Short answer

The hypotheses are H₀ : p = 0.12 and H_a : p< 0.12.

Step-by-step solution

Given information

The Department of Education reported that 12 percent of college students default on their loans.

Setting up the hypotheses

Let p denote the proportion of the student loan default rate this year.

It is required to test that the proportion p in the proportion p in the population has a specified valuep₀.

Here,

p₀= 0.12

The null hypothesis for the testing is given below:

H₀ : p = 0.12

That is, the population proportion of default rate is 0.12.

The alternative hypothesis for the testing is given below:

H_a : p < 0.12

That is, the population proportion of default rate is less than 0.12.