Question

The amounts of student loan debt college students have accumulated one year after graduating is normally distributed with  = $40,000 and  = $6,500. The federal government takes a sample of 625 people who graduated one year ago and finds that for this group of people the average amount of student loan debt accumulated was $35,500. Fannie Mae takes a sample of 729 people and finds the average credit debt is $37,250. Which of the findings is more likely?

Answer 1

Since the amount of student loan debt is normally distributed with known population standard deviation, we can compare the two sample distribution by calculating the z score. The z score is defined as the standardized difference between the sample and the population mean. Thus for the smaller value of the z score, the sample mean will be closer to the population mean.

From the survey data of the federal government,

Conclusion: The sample mean is approximately 17.31 standard deviation below the population mean.

From the survey data of the Fannie

Conclusion: The sample mean is approximately 11.42 standard deviation below the population mean.

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