Question: A plant produces rods with a specified .5 cm mean diameter. The standard deviation is unknown. A decision rule must be established for determining when to correct for over- or undersized output. The choice will be based on a sample of 100 rods, under the stipulation that there be only a 1% chance of taking corrective action when the mean diameter is exactly on target.

1. Set up the hypothesis testing to determine if a correction is necessary
2. What action should be taken if the sample average is .497 cm and sample standard deviation is .0075 cm?
3. Suppose that the sample average is .508 cm and sample standard deviation is .013. Construct a 99% confidence interval estimate for the mean diameter.
   Does this contain μ0?
4. What action should be taken?

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