Elementary Statistics (12th Edition)

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

Chapter 8 - Hypothesis Testing - 8-5 Testing a Claim About a Standard Deviation or Variance - Basic Skills and Concepts - Page 429: 4


a) $σ=1.8$, $σ\lt1.8$ b) $0.694$ c) We should reject it. d) We should accept it. e) It is effective.

Work Step by Step

a. The null hypothesis is the original situation, which is $σ=1.8$. The alternative hypothesis is $σ\lt1.8$, for this is what we want to verify. b) The test statistic equals: $\frac{(n−1)(s^2)}{σ^2}=0.694$ c) $0.694\gt 0.05$, hence we can see that we should reject the null hypothesis. d) We rejected the null hypothesis, hence it follows that we should accept the alternative hypothesis, which is the original claim. e) We accepted the alternative hypothesis, hence we can see that the change actually did help.
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