# Question: A loan officer compares the interest rates for 48 month fixed rate

A loan officer compares the interest rates for 48-month fixed-rate auto loans and 48-month variable- rate auto loans. Two independent, random samples of auto loan rates are selected. A sample of eight 48-month fixed-rate auto loans had 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 had loan rates as follows:

3.59% 2.75% 2.99% 2.50% 3.00%

a. 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.

b. Figure 10.7 gives the Excel output of using the equal variances procedure to test the hypotheses you set up in part a. Assuming that the normality and equal variances assumptions hold, use the Excel output and critical values to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48-month fixed-and variable-rate auto loans differ?

c. Figure 10.7 gives the p-value for testing the hypotheses you set up in part a. Use the p-value to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48-month fixed-and variable- rate auto loans differ?

d. Calculate a 95 percent confidence interval for the difference between the mean rates for fixed-and variable- rate 48-month auto loans. Can we be 95 percent confident that the difference between these means exceeds .4 percent? Explain.

e. Use a hypothesis test to establish that the difference between the mean rates for fixed- and variable- rate 48- month auto loans exceeds .4 percent. Use α equal to .05.

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 had loan rates as follows:

3.59% 2.75% 2.99% 2.50% 3.00%

a. 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.

b. Figure 10.7 gives the Excel output of using the equal variances procedure to test the hypotheses you set up in part a. Assuming that the normality and equal variances assumptions hold, use the Excel output and critical values to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48-month fixed-and variable-rate auto loans differ?

c. Figure 10.7 gives the p-value for testing the hypotheses you set up in part a. Use the p-value to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48-month fixed-and variable- rate auto loans differ?

d. Calculate a 95 percent confidence interval for the difference between the mean rates for fixed-and variable- rate 48-month auto loans. Can we be 95 percent confident that the difference between these means exceeds .4 percent? Explain.

e. Use a hypothesis test to establish that the difference between the mean rates for fixed- and variable- rate 48- month auto loans exceeds .4 percent. Use α equal to .05.

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