Probability/Statistics
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Smith Widget Company makes widgets for the medical industry. One particular customer requires widgets that meet FDA standards. One FDA standard requires Ztesting of at least 100 widgets at a time at the .08 level of significance. The specific standard requires that widgets be no smaller than a certain tolerance and no larger than a certain tolerance. The critical value(s) for such a test would be:

If you are doing a ztest, you look at a ztable for your cutoff or critical value(s). How do you translate .08 to a cutoff value from the table? It depends on whether the test is onetailed or twotailed. For a twotailed test (cutoff points at both tails), you split the .08 into .04 and .04 for both tails. (For a onetailed test, you don't split the value.) Some ztables will make it easier for you by showing values in the tails. Then you would look for your cutoffs according to the level given, remembering to split for twotailed tests. It may also help to have an index card with some commonly used cutoff values, so you don't have to look at the table each time.
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