A loan officer compares the interest rates for 48-monthfixed-rate auto loans and 48-month variable-rate auto loans. Twoindependent, random samples of auto loan rates are selected. Asample of eight 48-month fixed-rate auto loans and a sample of fivevariable-rate auto loans had the following loan rates:
| Fixed(%) | Variable(%) |
4.29 | 3.59 |
3.75 | 2.75 |
3.5 | 2.99 |
3.99 | 2.5 |
3.75 | 3 |
3.99 | |
5.4 | |
4 | |
Answer the following questions:
Let's define μFμF as the population mean loan rate forfixed-rate auto loans and
μVμV as the population mean loan rate for variable-rate autoloans.
a. The loan officer thinks the mean loan rates for fixed-rateauto loans is at least 1% greater than the mean loan rates for thevariable-rate auto loans. Set up the null and alternativehypotheses needed to determine whether this claim is correct.
H0: μFμF-μVμV (Click to select)≠0<1≠1≤ 1=0≥1>1>0≥0≤0=1<0
Ha: μFμF-μVμV (Click to select)≤1>1≠0=0≤0>0≠1<0<1≥1=1
b. What is the critical value rejection rule. (Assume unequalvariances and a significance level of 0.05.Answers should be in 4decimals.)
Critical value rule: Reject H0 if (Click to select)t<-talphat > t alphat > t alpha/2 or t <-t alpha/2 where thecritical value is .
c. What is the t test statistic and p-value? (4 decimals)
t=
p-value=
What is the value in the numerator of the test statistic?
What is the value in the denominator of the test statistic?
Which one of the following is the correct p-valuecalculation?(Click to select)2 x(1-t.inv(0.95,10))1-t.dist(0.430,10,true)t.dist(0.430,10,true)2 x(1-t.dist(0.430,10,true))t.inv(0.95,10)1-t.inv(0.95,10)
d. With 95% confidence we (Click toselect)cancannot  conclude that the mean loan rate forfixed-rate auto-loans is at least 1% greater than the loan rate forvariable-rate auto-loans.
e. We have (Click to select)extremely strongsomenoverystrongstrong evidence that the mean loan rates for fixed-rate autoloans is at least 1% greater than the mean loan rates for thevariable rate auto loans.
f. Calculate a 95 percent confidence interval for the differencebetween the mean rates for fixed-rate and variable-rate 48-monthauto loans.
_____ ≤  μFμF-μVμV  ≤ _____ (4decimals).
