Student loan debt has fluctuated over years, with signs indicating that the default rate may be increasing. Write the null and alternative hypothesis if you want to determine if the student loan default rate this year is more than $15\%$.

• A. $H_0:p=0.15$$H_a:p>0.15$
• B. $H_0:p=0.85$$H_a:p>0.85$
• C. $H_0:p>0.15$$H_a:p=0.15$
• D. $H_0:p>0.85$$H_a:p=0.85$

Answer: (A)

Verified step by step guidance

1. Identify the parameter of interest, which in this case is the student loan default rate. Denote this parameter as 'p'.
2. Understand the context: You want to test if the student loan default rate this year is more than 15%. This indicates a one-tailed test.
3. Formulate the null hypothesis (H0). The null hypothesis represents the status quo or no change. Here, it would be that the default rate is equal to 15%. In mathematical terms, H0: p = 0.15.
4. Formulate the alternative hypothesis (Ha). The alternative hypothesis represents the change or effect you are testing for. Here, it would be that the default rate is greater than 15%. In mathematical terms, Ha: p > 0.15.
5. Ensure that the hypotheses are mutually exclusive and collectively exhaustive, meaning they cover all possible scenarios regarding the default rate being equal to or greater than 15%.