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. Find 95% confidence interval for the population average debt. Confirm that the conclusion from the hypothesis test you did in part (a) is consistent with the conclusion you would draw from the confidence interval.

Answer 1

A) The null and aletrnative hypothesis is ,

Since , the population standard devitaion is known.

Therefore , use normal distribution.

The test statistic is ,

The critical values are ,

; From Z-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to conclude that the average debt load of graduating students with a bachelor's degree is equal to $17,000.

B) The 95% confidence interval for the population average debt is ,

Here , the value $17000 lies in the confidence interval.

Therefore , fail to reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to conclude that the average debt load of graduating students with a bachelor's degree is equal to $17,000.