Question

12. Suppose that 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 ? = 0.01.
a. State the null and alternative hypotheses.
b. Calculate the test statistic.
c. Find the critical value(s).
d. What do you conclude? Why?

Answer 1

12)

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 17000

H_a : 17000

= 18200

= 17000

= 4200

n = 34

Test statistic = z

= ( - ) / / n

= (18200 - 17000) / 4200 / 34

= 1.67

Test statistic = 1.67

= 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Critical values : -2.576 , 2.576

test statistic < critical vale

Fail to reject the null hypothesis .

There is not sufficient evidence .