Elementary Statistics (12th Edition)

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

Chapter 8 - Hypothesis Testing - 8-4 Testing a Claim About a Mean - Basic Skills and Concepts: 28

Answer

There is sufficient evidence to support that the mean is 120 volts.

Work Step by Step

$H_{0}:\mu=120$. $H_{a}:\mu\ne120.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{123.6625-120}{0.2404/\sqrt{40}}=96.355.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=40-1=39, hence P is less than 0.005. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than $\alpha=0.01$, because it is less than 0.005, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the mean is 120 volts.
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