Elementary Statistics (12th Edition)

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

Chapter 13 - Nonparametric Statistics - 13-2 Sign Test - Basic Skills and Concepts: 15

Answer

There is no difference.

Work Step by Step

The sample size is more than 25, hence the value of the test statistic: $z=\frac{(x+0.5)-n/2}{\sqrt n/2}=\frac{(123+0.5)-280/2}{\sqrt{280}/2}=-1.97.$ By using the table, the corresponding critical value: $z=\pm 2.575.$ If the value of the test statistic is in the rejection region, we reject the null hypothesis. -1.97 is between -2.575 and 2.575 hence we fail to reject the null hypothesis, hence there is no difference.
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