8 10 points eBook Print 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% 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) References Means and Std Deviations Level Number Fixed 5 Mean 4.03540 Std Dev 0.251785 Variable 5 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 Lower CL Dif Confidence -1.4187 0.95 Prob> t Prob (b) Figure 11.7 gives the JMP 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 JMP output and critical values to test these hypotheses by setting a 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? (Round your answer to 3 decimal places.) we will Extremely strong t = reject 6.543 with 8 df the null hypothesis in favor of the alternative for each a value. evidence that rates differ. (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 setting a 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? (Round your answer to 4 decimal places.) we will p-value = 0.0002 reject evidence. Extremely strong the null hypothesis in favor of the alternative for each a value. (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.) Confidence interval = [ 0.6793 1.4187]. Yes the entire interval is above .4. (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-uv s t= 0.4 versus Ha: f - v 0.4 Reject HO with a = .05.