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

Answer 1

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