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 (all written as percentages):

  

8.71

7.13

8.11

8.87

7.87

8.29

7.43

7.86

  

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

  

7.67

6.52

7.69

6.56

7.30

  

(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.

  

H0: µf − µv = versus Ha: µf − µv ≠

  

(b)

Use the data analysis tool in Excel 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) 0.001, 0.1, and 0.05 0.01, and 0.001 0.1, 0.05, and 0.01, but not at α = (Click to select)0.01, and 0.001 no values 0.1, 0.05, 0.01, and 0.001 0.1, and 0.05 0.05, and 0.001

  

(c)	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, 0.05, and 0.01 0.1, and 0.05 0.001 0.01, and 0.001 but not at α = (Click to select) 0.01, and 0.001 0.1, and 0.05 0.05, and 0.001 no values 0.1, 0.05, 0.01, and 0.001

  

(d)	Use a hypothesis test to establish that the difference between the mean rates for fixed− and variable−rate 48−month auto loans exceeds .4. Use α equal to .05. (Round your t answer to 3 decimal places and other answers to 1 decimal place.)

  

H0: µf − µv (Click to select) >, ≤, <, ≥  versus Ha: µf − µv (Click to select) ≤, <, ≥, >

t =

(Click to select) Reject or Do not reject  H0 with a  = .05.

Answer 1