Question

he amounts of student loan debt college students have accumulated one year after graduating is normally distributed with mu = $55,500 and sigma = $4,500. The federal government takes a sample of 289 people who graduated one year ago and finds that for this group of people the average amount of student loan debt accumulated was $45,250. Fannie Mae takes a sample of 144 people and finds the average credit debt is $39,000. Which of the findings is more likely?

Answer 1

Answer:

Given,

For federal government,

z = (x - u)/(s/sqrt(n))

substitute values

= (45250 - 55500)/(4500/sqrt(289))

= - 38.72

Here the sample mean is approximately 38.72 standard deviation below the population mean.

For Fannie ,

z = (x - u)/(s/sqrt(n))

substitute values

= (39000 - 55500)/(4500/sqrt(144))

= - 44

Here the sample mean is approximately 44 standard deviation below the population mean.

The sample mean from federal government's survey result is more closer to the population mean compared to the Fannie's survey result. Hence the federal government's finding is more likely compared to the Fannie's finding.