The bad debt ratio for a financial institution is defined to be the dollar value

ID: 3326157 • Letter: T

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. Suppose that a random sample of 7 Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 7%, 6%, 9%, 8%, 9%, 8%, and 6%.

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 aby setting equal to .01. Also, interpret the p-value of 0.0001 for the test. (Round your answers to 3 decimal places.)

(b)

Explanation / Answer

Assume
population mean(u)=3
given data
sample mean, x =7.5714
standard deviation, s =1.2754
number (n)=7
null, Ho: =3
alternate, H1: !=3
level of significance, = 0.01
from standard normal table, two tailed t /2 =3.707
since our test is two-tailed
reject Ho, if to < -3.707 OR if to > 3.707
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =7.5714-3/(1.2754/sqrt(7))
to =9.483
| to | =9.483
critical value
the value of |t | with n-1 = 6 d.f is 3.707
we got |to| =9.483 & | t | =3.707
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 9.4831 ) = 0.0001
hence value of p0.01 > 0.0001,here we reject Ho
ANSWERS
---------------
null, Ho: =3
alternate, H1: !=3
test statistic: 9.483
critical value: -3.707 , 3.707
decision: reject Ho
p-value: 0.0001
we have enough evidence to support the claim

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The bad debt ratio for a financial institution is defined to be the dollar value

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The bad debt ratio for a financial institution is defined to be the dollar value

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