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?
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?
Solution
The null and alternative hypotheses for this research question would be as follows:
Null Hypothesis (H0): p = 0.69 - This suggests that there is no significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014 compared to 2013. The proportion remains the same as in 2013, which is 69%.
Alternative Hypothesis (H1): p > 0.69 - This suggests that there is a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014 compared to 2013. The proportion is greater than 69%.
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