Engineers are often involved in estimating parameters. For example, there is an ASTM Standard E23 that defines a technique called the Charpy V-notch method for notched bar impact testing of metallic materials. The impact energy is often used to determine if the material experiences a ductile-to-brittle transition as the temperature decreases. Suppose that you have tested a sample of 10 specimens of a particular material with this procedure. You know that you can use the sample average to estimate the true mean impact energy μ. However, we also know that the true mean impact energy is unlikely to be exactly equal to your estimate. Reporting the results of your test as a single number is unappealing, because there is nothing inherent in that provides any information about how close it is to μ. Your estimate could be very close, or it could be considerably far from the true mean. A way to avoid this is to report the estimate in terms of a range of plausible values called a confidence interval. A confidence interval always specifies a confidence level, usually 90%, 95%, or 99%, which is a measure of the reliability of the procedure. So if a 95% confidence interval on the ...

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