Question

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 10 defaulted loans yielded a mean of $60,850 with a standard deviation of $16,100.22. Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years.

Answer 1

Answer: = ( $52,474.75 , $69,225.25)

Therefore at 90% confidence interval = ( $52,474.75 , $69,225.25)

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $60,850

Standard deviation r = $16,100.22

Number of samples n = 10

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

60,850+/-1.645(16,100.22/√10)

60,850+/-1.645(5091.336602979)

60,850+/-8375.248711901

$60,850+/-8375.248711901+/- $8375.25

= ( $52474.75 , $69225.25)

Therefore at 90% confidence interval = ( $52474.75 , $69225.25)