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 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: mu lessthanorequalto 3.5 % versus H_a: mu > 3.5 %. (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 3.5% when it actually is lessthanorequalto 3.5%. Type II: Conclude that Ohio's mean bad debt ratio is 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 a equal to 01. Also, interpret the p-value of 0.0004 for the test. (Round your answers to 3 decimal places.)

Explanation / Answer

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of variable
H0 : = 3.5
HA : > 3.5

Hypothesis test results:

Hence,

t = 6.125

Also,

Degrees of freedom = n - 1 = 7 - 1 = 6 and this is a right tailed test. So,

t.01 = 3.143

Variable Sample Mean Std. Err. DF T-Stat P-value var5 7.1428571 0.59476171 6 6.1249019 0.0004

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