Question

According to the National Science Foundation, individuals who graduated in 2010 with a doctoral degree had an average of $14,115 graduate debt. Assume that the standard deviation of graduate debt is $26,400. If we take a sample of 100 people who earned a doctoral degree in 2010.Calculate a 92% confidence interval for the average debt load of a student who graduated with a doctoral degree in 2010.

Answer 1

Solution :

sample size = n = 100

Degrees of freedom = df = n - 1 = 99

t /2,df = 1.769

Margin of error = E = t/2,df * (s /n)

= 1.769 * (26400 / 100)

Margin of error = E = 4670.1

The 92% confidence interval estimate of the population mean is,

- E < < + E

14115 - 4670.1 < < 14115 + 4670.1

9,444.9‬ < < 18,785.1‬

(9,444.9, 18,785.1‬)