# Setting up hypothesis tests for mean of a bad debt Ratio

I was given the following question a on an assignment.

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. A random sample of seven Ohio banks is selected. The bad debt ratios (written in percentages) for these banks are 7,4,6,7,5,4, and 9 percent.

# Question

$(a)$The mean bad dept ratio for federally insured banks is 3.5%. Federal banking officials claim that the mean debt ratio for Ohio banks is higher than the mean for all federally insured banks. Set up null and alternative hypotheses that should be used to statistically back up this claim

$(b)$ Assuming tht bad debt ratios for Ohio banks are normally distibuted, use the sample results given above to test the hypothesis you set up in part $(a)$ with $\alpha=0.01$

# My attempt

$(a)$ So I suppose the question wants me to set up null and alternative hypothesis as such.

$H_o:\mu> 0.035$ v.s $H_1: \mu \le 0.035$

Am I to assume that $\alpha=0.05$ or is simply setting it up as such enough?

$(b)$ I'm aware that the rejection point condition is:

# $|t| > t^{(n-1)}_{\alpha \over2}$ $\iff$ $|{\bar{y}-c \over s/\sqrt{n}}|>t^{n-1}_{\alpha\over 2}$

Do I set $\bar{y}={1\over{7}} \sum^{n=7}_{i=1} y_i =0.06$ and $c=0.035$ to find the test stat?

Usually one chooses the null hypothesis to be what one tries to reject. In this case I would do:

H_0: mu <= 0.035
H_1: mu > 0.035


as this formulates your hypothesis to testing whether or not the debt ratio of Ohio banks are identical to that of the federal banks.

In your answer to the second question you are dividing alpha (your significance level) by two in your critical value. This implies that you are conducting a two-tailed test. As you are only interested in testing if the debt ratio for Ohio banks is higher than that of Federal banks, not either higher or lower, you have to conduct a one-tailed test. More specifically a upper-tail test.

Also, it looks like you calculated the average of the Ohio banks debt ratios wrong. The sum of the rates divided by 7 is 6, not 5.8.

• Noted. An edit was made – Ploni Almoni Oct 9 '16 at 0:53