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 449: 3


a.) $H_{0}:p_{1}=p_{2}$ , $H_{1}:p_{1}\lt p_{2}$ b.) Based on $P$, we can conclude that children who are given the Salk vaccine are less likely to contract polio than those who were given a placebo.

Work Step by Step

a.) To identify the null hypothesis and the alternative hypothesis, we need to figure out whether the rate of polio was lower for those given the Salk vaccine. $H_{0}$ represents the null hypothesis. $H_{1}$ represents the alternative hypothesis. $P_{1}$ represents the children given the vaccine. $P_{2}$ represents the children given the placebo. $H_{0}:p_{1}=p_{2}$ says that the number of children given the vaccine must equal those given the placebo. $H_{1}:p_{1}\lt p_{2}$ says that the number of children who contracted polio while given the placebo must be greater than those who were given the vaccine and contracted polio. b.) The $P$ value given was less than 0.001, so this means that it is very small. Therefore we can conclude that the children given the Salk vaccine have significantly lower chances of contracting polio than those who are given the placebo.
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