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?

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.

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.

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.

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.

The true statement regarding the hypothesis from the Department of Education is D. Because the p-value is greater than α, we fail to reject the null hypothesis.

How to illustrate the p-value?

From the information given, the test statistic will be:

= (18200 - 17000) / (4200/✓34)

= 1.67

In this case, the null hypothesis will be rejected as z calculated is greater then the z critical and when p value is less than the given level of alpha, we accept the null hypothesis.

Therefore, we fail to reject the null hypothesis.

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