Question: A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is approximately normally distributed with the population standard deviation \(\sigma=1.5 \mathrm{~mm}\). A random sample of 20 rings has a sample mean diameter of \(75.012 \mathrm{~mm}\).

1. Find a \(95 \%\) lower limit for the true mean piston diameter.
2. Based on the confidence limit which of the following hypothesis would choose, and why? Ho: \(\mu \leq 74 \quad\) H1: \(\mu>74\) Use \(\alpha=.05\)

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