Instructions
Hypothesis Testing
A loan officer wants to compare the interest rates for 48-month fixed-rate auto loans and 48-month variable-rate auto loans.
Two independent, random samples of auto loans are selected. A sample of eight 48-month fixed-rate auto-loans have the following loan rates:
4.29%, 3.75%, 3.50%, 3.99%, 3.75%, 3.99%, 5.40%, 4.00%
while a sample of five 48-month variable-rate auto loans have the loan rates as follows:
3.59%, 2.75%, 2.99%, 2.50%, 3.00%
Test statistic and the corresponding p value s are listed below:
| Test Statistic | p Value |
| 3.7431 | 0.0032 |
Tasks:
- Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month fixed-rate and variable-rate auto loans differ.
- Identify the test you will apply to test the hypothesis. Justify your choice.
- Choose an appropriate level of significance.
- Define type I and type II errors in the context of your hypotheses.
- State your decision regarding the hypothesis.
- State the conclusion.