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 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances - Review Exercises - Section 9-2 - Page 541: 3

Answer

Yes, see explanations.

Work Step by Step

We are given $n1=20, \bar X1=172/20=8.6, s1=3.6$ and $n2=30, \bar X2=366/30=12.2, s2=4.2$ a. State the hypotheses and identify the claim. $H_o: \mu1-\mu2=0$ $H_a: \mu1-\mu2 \ne 0$ (claim, two tail test) b. Find the critical value(s). $\alpha/2=0.005, df=19, |t_c|=2.861$ c. Compute the test value. $z=\frac{8.6-12.2-0}{\sqrt {\frac{3.6^2}{20}+\frac{4.2^2}{30}}}=-3.24$ d. Make the decision. Since $z\lt -2.861$, we reject the null hypothesis. e. Summarize the results. At α= 0.01, a difference in means can be concluded.
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