## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 8 - Hypothesis Testing - Review - Review Exercises - Page 434: 10

#### Answer

There is sufficient evidence to support that the mean less than 1000.

#### Work Step by Step

$H_{0}:\mu=1000$. $H_{a}:\mu <1000.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{653.8-1000}{76.0671/\sqrt{5}}=-10.177.$ 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=5-1=4, 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 less than 1000.

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