Question

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.

Answer 1