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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 Z-testing 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 z-test, you look at a z-table 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 one-tailed or two-tailed. For a two-tailed test (cutoff points at both tails), you split the .08 into .04 and .04 for both tails. (For a one-tailed test, you don't split the value.) Some z-tables 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 two-tailed 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.