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

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 6%, 9%, 5%, 7%, 5%, 7%, and 6%.

(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.)

H0: <  % versus Ha: >  %.

(a-2) Discuss the meanings of a Type I error and a Type II error in this situation.

(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 equal to .01. Also, interpret the p-value of 0.0007 for the test. (Round your answers to 3 decimal places.)

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%.

Explanation / Answer

Given that,

population mean(u)=3.5

sample mean, x =6.4286

standard deviation, s =1.3973

number (n)=7

null, Ho: <3.5

alternate, H1: >3.5

level of significance, = 0.01

from standard normal table,right tailed t /2 =3.143

since our test is right-tailed

reject Ho, if to > 3.143

we use test statistic (t) = x-u/(s.d/sqrt(n))

to =6.4286-3.5/(1.3973/sqrt(7))

to =5.545

| to | =5.545

critical value

the value of |t | with n-1 = 6 d.f is 3.143

we got |to| =5.545 & | t | =3.143

make decision

hence value of | to | > | t | and here we reject Ho

p-value :right tail - Ha : ( p > 5.5452 ) = 0.00073

hence value of p0.01 > 0.00073,here we reject Ho

ANSWERS

---------------

(a-1) null, Ho: <3.5 , alternate, H1: >3.5

(a-2) Type I: Conclude that Ohio’s mean bad debt ratio is > 3.5% when it actually is 3.5%.

Type II: conclude that Ohio’s mean bad debt ratio is < 3.5% when it actually is > 3.5%.

test statistic: 5.545

critical value: 3.143

decision: reject Ho

p-value: 0.00073

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