Question

# The Department of Education would like to test the hypothesis that the average debt load of...

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]

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]

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