Question

does going to a private university increase the chance that a student will graduate with student loan debt? a national poll by the institute for college access and success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt.
a researcher wanted to see if there was a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014. suppose that the researcher surveyed 1500 graduates of public and nonprofit universities and found that 71% of graduates had student loan debt in 2014.
let p be the proportion of all graduates of public nonprofit universities that graduated with student loan debt. what are the appropriate null and alternative hypotheses for this research question?
a.
( h_{0}:p = 0.69 )
( h_{a}:p
eq 0.69 )
b.
( h_{0}:p = 0.69 )
( h_{a}:p > 0.69 )
c.
( h_{0}:p = 0.71 )
( h_{a}:p
eq 0.71 )
d.
( h_{0}:mu = 0.69 )
( h_{a}:mu > 0.69 )

Explanation:

Step1: Understand null hypothesis

The null hypothesis \(H_{0}\) is a statement of no change. Here, the proportion in 2013 is \(0.69\), so \(H_{0}:p = 0.69\).

Step2: Determine alternative hypothesis

The researcher wants to check for a significant increase. So the alternative hypothesis \(H_{a}\) is \(p>0.69\) (right - tailed test).

• Option A has a two - tailed alternative (\(p

eq0.69\)) which is not for an increase.

• Option C has the null hypothesis as \(p = 0.71\) which is the sample proportion in 2014 (not the base value from 2013).
• Option D uses \(\mu\) (for mean) instead of \(p\) (for proportion).

Answer:

B. \( H_{0}:p = 0.69\), \( H_{a}:p>0.69\)