Question

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor’s degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be __________________.

Multiple Choice

• [$16,279.7, $17,720.3]

• [$14,839.1, $19,160.9]

• [$16,788.22, $19,611.78]

• [$14,118.9, $19,881.2]

Answer 1

Here

a = 0.05 so confidence level c = 0.95

Also population standard deviation is given

We have to find 95% confidence interval for population mean

xbar - Z​​​​​​a/2*(/√n) < < xbar + Z​​​​​​a/2*(/√n)

For a = 0.05 , Z​​​​​​a/2 = Z​​​​​​0.025 = 1.96

18200 -1.96*(4200/√34) < < 18200+1.96*(4200/√34)

16788.22 <   < 19611.78

So the required confidence interval is [16788.22, 19611.78]