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180% 3.198 3.22% th fixed-rate auto loans had loan rates as fo 1958 3.659 4.20% he Equality of Mean Loan Rates for ixed 48-Month Auto Loans

180% 3.198 3.22% th fixed-rate auto loans had loan rates as fo 1958 3.659 4.20% he Equality of Mean Loan Rates for ixed 48-Month Auto Loans

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Parts D and E

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: 2.50% 3.12% 2.880% 3.198 3.22% while a sample of five 48-month fixed-rate auto loans had loan rates as follows: 4.028* 3.93% 4.3958 3.658 4.20% Figure 11.7 JMP Output of Testing the Equality of Mean Loan Rates for Variable and Fixed 48-Month Auto Loans Means and Std Deviations Level Fixed Variable t Test Variable-Fixed Assuming equal variances Difference Std Err Dif Upper CL Dif Lover CL Dif Confidence HO: uf- uv Number 5 5 t= p-value= we will Extremely strong -1.0586 0.1841 -0.6341 -1.4831 0.95 (a) Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month variable-rate and fixed-rate auto loans differ, Confidence interval= HO: uf- uv Mean 4.04060 2.98200 t Ratio DE (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.) Prob > |t| Prob > t Prob t ✔ Answer is complete and correct. 0 versus Ha: uf- uv 5.751 with 8 df we will reject ✔ the null hypothesis in favor of the alterative for each a value. Extremely strong ✔ evidence that rates differ. 0.0004 reject evidence. | || Std Dev 0.300699 0.281055 (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.) -5.75102 8 0.0004 0.9998 <0.0002. 0 ✔ Answer is complete and correct. (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.) 1. ✔ Answer is complete and correct. the null hypothesis in favor of the altemative for each a value. HO with a = .05. versus Ha: uf- uv J. (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.) the entire interval is 4.
Transcribed Image Text: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: 2.50% 3.12% 2.880% 3.198 3.22% while a sample of five 48-month fixed-rate auto loans had loan rates as follows: 4.028* 3.93% 4.3958 3.658 4.20% Figure 11.7 JMP Output of Testing the Equality of Mean Loan Rates for Variable and Fixed 48-Month Auto Loans Means and Std Deviations Level Fixed Variable t Test Variable-Fixed Assuming equal variances Difference Std Err Dif Upper CL Dif Lover CL Dif Confidence HO: uf- uv Number 5 5 t= p-value= we will Extremely strong -1.0586 0.1841 -0.6341 -1.4831 0.95 (a) Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month variable-rate and fixed-rate auto loans differ, Confidence interval= HO: uf- uv Mean 4.04060 2.98200 t Ratio DE (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.) Prob > |t| Prob > t Prob t ✔ Answer is complete and correct. 0 versus Ha: uf- uv 5.751 with 8 df we will reject ✔ the null hypothesis in favor of the alterative for each a value. Extremely strong ✔ evidence that rates differ. 0.0004 reject evidence. | || Std Dev 0.300699 0.281055 (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.) -5.75102 8 0.0004 0.9998 <0.0002. 0 ✔ Answer is complete and correct. (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.) 1. ✔ Answer is complete and correct. the null hypothesis in favor of the altemative for each a value. HO with a = .05. versus Ha: uf- uv J. (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.) the entire interval is 4.
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