## Related questions with answers

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:

$\begin{array}{llll} 4.29 \% & 3.75 \% & 3.50 \% & 3.99 \% \\ 3.75 \% & 3.99 \% & 5.40 \% & 4.00 \% \end{array}$

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

$\begin{array}{llll} 3.59 \% & 2.75 \% & 2.99 \% & 3.00 \% \\ \end{array}$

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? Explain.

Solution

VerifiedWhen we want to compute a $100(1-\alpha)\%$ confidence interval for $\mu_1-\mu_2$ , we have to use this formula:

$\left[ (\=x_1-\=x_2) \pm t_{\alpha/2} \sqrt{s_p^2 \left(\frac{1}{n_1}+\frac{1}{n_2}\right)} \right].$

We use this formula when we know that variances are equal.

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