Answer
Yes, see explanations.
Work Step by Step
a. State the hypotheses and identify the claim.
$H_o: \mu=18000$
$H_a: \mu\lt 18000$ (claim, left tail test)
b. Find the critical value(s).
$\alpha=0.01, z_c=-3.1$
c. Compute the test value.
From the data set we have $\bar X=16298.4$
and $z=\frac{16298.4-18000}{2605/\sqrt {30}}=-3.58$
d. Make the decision.
Since $z\lt z_c$ and is in the rejection region, we should reject the null hypothesis and support the claim.
e. Summarize the results.
There is sufficient evidence at a= 0.01 to conclude that the population mean debt at graduation
is less than 18,000.
