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In an experiment to measure the lifetimes of parts
Chapter 6, Problem 1E(choose chapter or problem)
In an experiment to measure the lifetimes of parts manufactured from a certain aluminum alloy, 73 parts were loaded cyclically until failure. The mean number of kilocycles to failure was 783, and the standard deviation was 120. Let \(\mu\) represent the mean number of kilocycles to failure for parts of this type. A test is made of \(H_o:\mu\leq 750\) versus \(H_1: \mu>750\).
a. Find the P-value.
b. Either the mean number of kilocycles to failure is greater than 750, or the sample is in the most extreme _______ % of its distribution.
Questions & Answers
QUESTION:
In an experiment to measure the lifetimes of parts manufactured from a certain aluminum alloy, 73 parts were loaded cyclically until failure. The mean number of kilocycles to failure was 783, and the standard deviation was 120. Let \(\mu\) represent the mean number of kilocycles to failure for parts of this type. A test is made of \(H_o:\mu\leq 750\) versus \(H_1: \mu>750\).
a. Find the P-value.
b. Either the mean number of kilocycles to failure is greater than 750, or the sample is in the most extreme _______ % of its distribution.
ANSWER:Step 1 of 3
To find the P-value
The sample size is \(n=73\)
The sample mean is \(\bar{x}=783\)
Standard deviation is \(\sigma=120\)
Therefore, the z-value is
\(\begin{aligned} z & =\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\ & =\frac{783-750}{\frac{120}{\sqrt{73}}} \\ & =2.3496 \\ & \approx 2.35 \end{aligned} \)