## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 8 - Hypothesis Testing - 8-4 Testing a Claim About a Mean - Basic Skills and Concepts: 27

#### Answer

There is sufficient evidence to support that the mean weight is less than 83.

#### Work Step by Step

$H_{0}:\mu=83$. $H_{a}:\mu <83.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{65.0597-83}{11.2854/\sqrt{67}}=-13.012.$ 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=67-1=66, 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 weight is less than 83.

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