Answer to Question #258212 in Statistics and Probability for mir

Question

the bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made.

Answer 1

The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of seven Ohio banks is selected and that the bad debt ratios (written in percentages) for these banks are 7%, 4%, 6%, 7%, 5%, 4%, and 9%. Banking officials claim that the mean bad debt ratio for all Midwestern banks is 7% and that the mean debt ratio for Ohio banks is lower. Is this a correct claim?

$H_0: \mu = 7 \\ H_1: \mu < 7 \\ \bar{x} = 6 \\ s = 1.826 \\ n=7$

Test-statistic

$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t = \frac{6-7}{1.826 / \sqrt{7}} = -1.449$

P-value = P(t < -1.449) = 0.0988

Since P-value is greater then α=0.05 we fail to reject the null hypothesis.

There is enough evidence to support the claim. The claim is correct.