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 9-4 - Page 541: 9


No, see explanations.

Work Step by Step

Given $n1=200, X1=49, \hat p1=49/200=0.245, n2=200, X2=62, \hat p2=62/200=0.31$ a. State the hypotheses and identify the claim. $H_o: p1=p2$ $H_a: p1\ne p2$ (claim, two tail test) b. Find the critical value(s $\alpha/2=0.025, |z_c|=2.81$ c. Compute the test value. $\bar p=\frac{49+62}{200+200}=0.2775, \bar q=1-\bar p=0.7225,$ $z=\frac{0.245-0.31-0}{\sqrt {0.2775\times0.7225\times(1/200+1/200)}}=-1.45$ d. Make the decision. As $z>-2.81$, we do not reject the null hypothesis. e. Summarize the results. At the 0.05 level of significance, there is not sufficient evidence to conclude a difference in proportions.
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