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 Department of Education would like to set  α = 0.05. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is

		more than the absolute value of the critical value, we can conclude that the average student debt load is not equal to $17,000.
		less than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000.
		less than the absolute value of the critical value, we can conclude that the average student debt load is not equal to $17,000.
		more than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000.

Answer 1

null hypothesis:Ho μ		=	17000
Alternate Hypothesis:Ha μ		≠	17000
for 0.05 level with two tail test , critical z=			1.960
Decision rule:reject Ho if absolute test stat|z|>1.96
	population mean μ=	17000
	sample mean 'x̄=	18200.000
	sample size    n=	34.00
	std deviation σ=	4200.000
	std error ='σx=σ/√n=	720.2941
	test stat z = '(x̄-μ)*√n/σ=	1.67

since test statistic does not falls in rejection region we fail to reject null hypothesis

less than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000.