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. Which one of the following statements is true?
A)Because the p-value is less than α, we fail to reject the null hypothesis and conclude that the average debt load is not equal to $17,000.
B)Because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
C)Because the p-value is greater than α, we fail to reject the null hypothesis and conclude that the average debt load is equal to $17,000.
D)Because the p-value is less than α, we reject the null hypothesis and conclude that the average debt load is equal to $17,000.

Question

Quizplus · Accepted Answer

B) is correct because when the p-value is greater than the significance level (α), the decision is to fail to reject the null hypothesis. This means there is not enough evidence to conclude a difference from the hypothesized mean, but it does not prove the null hypothesis to be true.

The Department of Education Would Like to Test the Hypothesis