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Your company's widget machine broke. The repair company claims that it is fixed and properly calibrated so that the defective widget production rate is 1% or less. You plan to use a test run to confirm the repair company's report.
1. You want you to select the test run size so that the standard error of the mean defective production rate is 0.2%. Assume the defective rate is 1% (i.e. p = 0.01). How large must the test run be?
2. You run a test of the size you determined in the prior question and find that the proportion of defective widgets is 1.40%. Based on a one-sided test, can you reject the null hypothesis that the machine's defective production rate is 1% or less with 99% confidence?
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