Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 8 - Hypothesis Testing - Review Exercises - Section 8-2 - Page 480: 3


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.
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