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 five 48-month variable-rate auto loans had the following loan rates:

2.6%

3.07%

2.872%

3.24%

3.15%

while a sample of five 48-month fixed-rate auto loans had loan rates as follows:

4.032%

3.85%

4.385%

3.75%

4.16%

4 t= (6.543) X with 8 df we will reject the null hypothesis in favor of the alternative for each a value. Extremely strong V evidence that rates differ. 7.22/10 points awarded Scored (c) Figure 11.7 gives the p-value for testing the hypotheses you set up in part a. Use the p-value to test these hypotheses by setti 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 eBook (Round your answer to 4 decimal places.) Print p-value = 0.0002 References we will reject the null hypothesis in favor of the alternative for each a value. Strong X evidence. (d) Calculate a 95 percent confidence interval for the difference between the mean rates for fixed- and variable-rate 48-month au loans. Can we be 95 percent confident that the difference between these means exceeds .4 percent? (Round your answers to 4 decimal places.) Confidence interval = (0.6793) X (1.4187) X Yes the entire interval is above .4.p-value = 0.0002 we will reject the null hypothesis in favor of the alternative for each a value. Strong X evidence. 7.22/10 points awarded Scored (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? (Round your answers to 4 decimal places.) eBook Print Confidence interval = (0.6793) X (1.4187) x ]. Yes , the entire interval is above 4.4. References (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 a equal to .05. (Round your t answer to 4 decimal places and other answers to 1 decimal place.) HO: uf - HV S 0.4 versus Ha: uf - Uv > 0.4 t = 4.0482 X Reject HO with a = .05.Click here for the Excel Data File FIGURE 11.7 JMP Output of Testing the Equality of Mean Loan Rates for Variable and Fixed 48-Month Auto Loans (for Exercise 11.12) Means and Std Deviations Level Number Mean Std Dev Fixed 4.03540 0.251785 Variable 2.98640 0.255176 t Test Variable-Fixed Assuming equal variances Difference -1.0490 t Ratio -6.54321 Std Err Dif 0.1603 DF 8 Upper CL Dif -0.6793 Prob > Itl 0.0002* Lower CL Dif -1.4187 Prob > t 0.9999 Confidence 0.95 Prob