A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years.A random sample of 20 defaulted loans yielded a mean of $67,918 with a standard deviation of $16,552.40.Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years.

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we will use the formula:

CI = x̄ ± t*(s/√n)

Where, 
x̄ = sample mean = $67,918 
s = sample standard deviation = $16,552.40 
n = sample size = 20

To find the t-value, we need to look up the corresponding value from the t-distribution table with (n-1) degrees of freedom and a 90% confidence level. For this sample size (n=20) and the given confidence level, the degrees of freedom is (n-1) = 19. From the t-distribution table, the t-value is 1.729.

Now, substituting the values in the formula, we get:

CI = $67,918 ± 1.729*($16,552.40/√20)
CI = $67,918 ± $7,401.97

Therefore, the 90% confidence interval for the mean balance of defaulted loans over the past three years is [ $61,516.03 , $74,319.97 ].

Hence, the best choice is E.

A Federal Bank Examiner Is Interested in Estimating the Mean