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A Design Engineer Wants to Construct a Sample Mean Chart

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A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:  Service Life (hours)   Sample 149550050550025255155055153470480460470\begin{array} { r } { \text { Service Life (hours) } }\\\begin{array} { l l l l l } \text { Sample } & \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}\end{array} If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error) ?

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Definitions:

Price Level

The average of current prices across the entire spectrum of goods and services produced in the economy.

Low Supplier Power

Refers to a market condition where suppliers have limited control over the price and terms of products and services due to high competition or low demand.

Threat from Substitutes

The potential for consumers to switch to alternative products that fulfill the same need, affecting demand.

Levels of Rivalry

Levels of rivalry refer to the intensity and number of competitors in a market or industry, impacting the competitive dynamics and strategy decisions of firms.

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