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% 2.8803.19% 3.22%while a sample of five 48-month fixed-rate auto loans had loan rates as follows:4.028% 3.93% 4.395% 3.65€Figure 11.7JMP Output of Testing the Equality of Mean Loan Rates forVariable and Fixed 48-Month Auto LoansMeans and Std DeviationsLevelFixedVariablet TestwwwVariable-FixedAssuming equal variancesDifferenceStd Err DifUpper CL DifLower CL DifConfidenceHO: uf- uv=we willwe willNumber55t=p-value=Confidence interval=HO: uf- uv-1.05860.1841-0.6341-1.48310.95(a) Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month variable-rate and fixed-rateauto loans differ.t=4.20%(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 thatthe normality and equal variances assumptions hold, use the JMP output and critical values to test these hypotheses by setting aequal 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.)Mean4.040602.98200t RatioDFevidence.Prob > tProb> tProbt(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 aequal 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.)[versus Ha: uf- uv #Std Dev0.3006990.281055-5.75102with 8 dfthe null hypothesis in favor of the alternative for each a value.evidence that rates differ.80.0004*0.9998<0.0002*(d) Calculate a 95 percent confidence interval for the difference between the mean rates for fixed- and variable-rate 48-month autoloans. Can we be 95 percent confident that the difference between these means exceeds .4 percent? (Round your answers to 4decimal places.)the null hypothesis in favor of the alternative for each a value.HO with a = .05.(e) Use a hypothesis test to establish that the difference between the mean rates for fixed- and variable-rate 48-month auto loansexceeds .4 percent. Use a equal to .05. (Round your t answer to 4 decimal places and other answers to 1 decimal place.)versus Ha: uf- uvthe entire interval is4.

The null hypothesis is a statement of no difference and the alternative hypothesis is the…

Answered: A loan officer compares the interest…

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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