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 7 Ohio banks is selected and that the bad debt ratios (written
as percentages) for these banks are 5%, 8%, 9%, 9%, 6%, 6%, and
7%.
(a-1) Banking officials claim that the mean bad
debt ratio for all Midwestern banks is 3.5 percent and that the
mean bad debt ratio for Ohio banks is higher. Set up the null and
alternative hypotheses needed to attempt to provide evidence
supporting the claim that the mean bad debt ratio for Ohio banks
exceeds 3.5 percent. (Round your answers to 1 decimal
place. Omit the "%" sign in your
response.)
H_{0}: μ < % versus
H_{a}: μ > %.
(a-2) Discuss the meanings of a Type I error
and a Type II error in this situation.
Type I: Conclude that Ohio’s mean bad debt ratio is (Click to select)>≤ 3.5% when it actually is ≤ 3.5%. |
Type II: Conclude that Ohio’s mean bad debt ratio is (Click to select)≤> 3.5% when it actually is > 3.5%. |
(b) Assuming that bad debt ratios for Ohio banks
are approximately normally distributed, use critical values and the
given sample information to test the hypotheses you set up in part
a by setting α equal to .01. Also, interpret the
p-value of 0.0004 for the test. (Round your
answers to 3 decimal places.)
t | |
t._{01} | |
Since t._{01} (Click to select)<>
t, (Click to select)do not rejectreject H_{0}
.
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