Elementary Statistics (12th Edition)

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

Chapter 8 - Hypothesis Testing - 8-3 Testing a Claim About a Proportion - Basic Skills and Concepts: 19

Answer

There is not sufficient evidence to support that cell phone users should be concerned about cancer of the brain or nervous system.

Work Step by Step

$H_{0}:p=0.00034$. $H_{a}:p\ne0.00034$ $\hat{p}$ is the number of objects with a specified value divided by the sample size. Hence $\hat{p}=\frac{x}{n}=\frac{135}{420095}=0.0003214.$ The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.0003214-0.00034}{\sqrt{0.00034(1-0.00034)/420095}}=-0.65.$ The P is the probability of the z-score being more than 0.65 or less than -0.65 is the sum of the probability of the z-score being less than -0.65 plus 1 minus the probability of the z-score being less than 0.65, hence:P=0.2578+1-0.7422=0.5156. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.5156 is more than $\alpha=0.05$, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to support that cell phone users should be concerned about cancer of the brain or nervous system.
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