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 - Beyond the Basics: 29

Answer

There is sufficient evidence to support that the mean number of chocolate chips is less than 24.

Work Step by Step

$H_{0}:\mu=24$. $H_{a}:\mu < 24.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{19.6-24}{3.8/\sqrt{40}}=-7.323$ The P-value is the probability of z being less than -7.323, hence P is 0.0001. 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 $\alpha=0.05$, because it is 0.0001, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the mean number of chocolate chips is less than 24.
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