A loan officer compares the interest rates for 48-month fixed-rate auto loans an

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 fixedrate auto loans had the following loan rates:

8.69%

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.

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 equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48month fixed and variablerate auto loans differ?(Round your answer to 3 decimal places.)

Figure 10.7 gives the pvalue for testing the hypotheses you set up in part a. Use the pvalue to test these hypotheses by setting equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48month fixed and variablerate auto loans differ? (Round your answer to 4 decimal places.)

Calculate a 95 percent confidence interval for the difference between the mean rates for fixed and variablerate 48month 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.)

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

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 fixedrate auto loans had the following loan rates:

Explanation / Answer

a) H0:muf-muv=0 versus H1: muf-muv not equal to 0.

b) t=2.557885, test statistic falls in critical zone, 2.200985. Reject H0at alph=0.05, 0.1.

Strong evidence.

c) P value=0.026619, is less than alpha=0.05, 0.1, Reject H0 at alpha=0.05, 0.1. Strong evidence.

d) 95% c.i=(Xbarf-Xbarv)+-tcritical *SE(Xbarf-Xbarv)=(7.99875-7.31600)+-2.201*0.4682=0.68275+-1.0305=-0.34775 to 1.71325

e) H0: muf-muv<=0.04 versus H1:muf-muv>0.04

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