Question

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: 8.65% 7.83% 7.34% 7.59% 8.66% 9.45% 9.22% 7.58% while a sample of five 48−month variable−rate auto loans had loan rates as follows: 7.29% 6.94% 6.91% 6.89% 7.63% Figure 10.7 Excel Output of Testing the Equality of Mean Loan Rates for Fixed and Variable 48-Month Auto Loans t-Test: Two-Sample Assuming Equal Variances Fixed-Rate (%) Variable-Rate (%) Mean 8.29000 7.13200 Variance .655029 .10442 Observations 8 5 Pooled Variance .454807 Hypothesized Mean Difference 0 df 11 t Stat 3.011988 P(T<=t) one-tail .005912 t Critical one-tail 1.79588 P(T<=t) two-tail .011824 t Critical two-tail 2.200985

(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.

H_f – µ_a: µ_f – µ_v =

(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? (Round your answer to 3 decimal places.)

t = with 11 df

Reject H₀ at α = (Click to select)0.01, and 0.0010.1, and 0.050.0010.1, 0.05, and 0.01, but not at α = (Click to select)0.05, and 0.0010.1, 0.05, 0.01, and 0.001no values0.01, and 0.0010.1, and 0.05

(Click to select)NoStrongExtremely strongVery strong evidence that rates 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? (Round your answer to 4 decimal places.)

p–value =

Reject H₀ at α = (Click to select)0.1, and 0.050.1, 0.05, and 0.010.01, and 0.0010.001 but not at α = (Click to select)0.01, and 0.001no values0.1, and 0.050.1, 0.05, 0.01, and 0.0010.05, and 0.001

(Click to select)NoExtremely strongVery strongStrong evidence.

(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 3 decimal places. Negative value should be indicated by a minus sign.)

Confidence interval = [ , ]. (Click to select)YesNo, the entire interval is (Click to select)abovenot above .40.

(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. (Round your t answer to 3 decimal places and other answers to 1 decimal place.)

H₀: µ_f – µ_v (Click to select)≥><≤  versus H_a: µ_f – µ_v (Click to select)<≤>≥

t =

(Click to select)Do not rejectReject H₀ with a = .05.

Answer 1