Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 9 - Inferences from Two Samples - 9-2 Two Proportions - Basic Skills and Concepts - Page 452: 15


a) The claim is supported. b) The claim is supported. c) The treatment is effective.

Work Step by Step

a) We want to see if the mean is different to $\frac{29}{148}=0.1959$, so we know $H_0:μ=0.1959$ and $H1:μ\gt0.1959$. We now use a Ti-84 calculator. To solve, go to "Stat," then "Tests," and then select "Stats." Doing this, we can find that the critical value and use a z-table calculator to find that $p=0.0000\lt0.05$, hence the claim is valid. b) We use a ti-84 calculator to find the confidence interval. To do this, we press “Stat” and then select “Tests.” Next, we select “2-PropZInt” to conduct the test. Doing this, we can find that the $0.467\lt \mu\lt0.687$. This is bigger than $0$, meaning that the treatment does improve the patient's well-being. c) The results show that the treatment works and does, indeed, help treat headaches.
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