Answer:
Step-by-step 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.