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Lesson: Chapter 10 Review
TMER WASHINGTON
Question 7 of 9. Step 1 of 3
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2
A manufacturer must test that his bolts are $4.00 \mathrm{~cm}$ long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 81 randomly selected bolts off the assembly line, he calculates the sample mean to be $3.97 \mathrm{~cm}$. He knows that the population standard deviation is $0.14 \mathrm{~cm}$. Assuming a level of significance of 0.01 , is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.
\[
\begin{array}{l}
H_{0}: \mu=4.00 \\
H_{a}: \mu \quad 4.00
\end{array}
\]
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Final Answer: \n\[\begin{array}{l} H_{0}: \mu=4.00 \ H_{a}: \mu \neq 4.00 \end{array}\]
Step 1 ：The question is asking to state the null and alternative hypotheses for the test. The null hypothesis is usually a statement of no effect or no difference. In this case, the null hypothesis is that the mean length of the bolts is 4.00 cm. The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the mean length of the bolts is not 4.00 cm.
Step 2 ：Final Answer: \n\[\begin{array}{l} H_{0}: \mu=4.00 \ H_{a}: \mu \neq 4.00 \end{array}\]
