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. (a) Perform a hypothesis test showing all steps.

Ho :- mu = 17000

Ha :- mu not equal 17000

Xbar=18200 , n=34, sigma =4200, alpha = 0.05

This is one sample mean Z test

Test statistics

Z = ( xbar - mu ) / ( sigma / sqrt ( n ) )

Z = ( 18200 - 17000 ) / ( 4200 / sqrt ( 34 ) )

Z = 1.6660

Decision rules

Reject Ho if

Z stat > Z critical

Z = 1.6660 < 1.96 = Z critical

We do not reject Ho

P value = 2* P ( Z > | 1.6660 | ) = 0.0957

P value = 0.0957 > 0.05 = alpha

We do not reject Ho

Conclusion :- there is sufficient evidence to support the claim that the average debt load of graduating students with a bachelor's degree is equal to \$17,000

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