Answer:
Explanation:
From the information given:
Consider X to be the random variable denoting the bad debt ratios for Ohio Bank.
Then,

Thus the null hypothesis and the alternative can be computed as:
Null hypothesis:

Alternative hypothesis

The type I and type II error is as follows:
Type I:
The mean bad debt ratio is > 3.5% when it is not
Type II:
The mean bad debt ratio is ≤ 3.5% when it is not.
The test statistics can be calculated by using the formula:

where;
sample size n = 7
mean = 6+8+5+9+7+5+8 = 48
sample mean

= 6.86
sample standard deviation is :


s = 1.573
population mean

Therefore, the test statistics is :




t = 5.660
At significance level of 0.01
P - value = P(T > 5.66)
P - value = 1 - (T < 5.66)
P - value = 1 - 0.9993
P-value = 0.0007
Therefore, since
, we reject the null hypothesis and conclude that the claim that the mean bad debt ratio for Ohio banks is higher than the mean for all financial institutions is true.