Acme Bicycle Company makes derailleurs for mountain bikes. Usually no more than 4% of these parts are defective, but occasionally the machines that make them get out of adjustment and the rate of defectives exceeds 4%. To guard against this, the chief quality control inspector takes a random sample of 130 derailleurs each week and checks each one for defects. If too many of these parts are defective, the machines are shut down and adjusted. To decide how many parts must be defective to shut down the machines, the company’s statistician has set up the hypothesis test
Ho: = p < .04 versus H1: p > .04
Where p is the proportion of defectives among all derailleurs being made currently. Rejection of H0 would call for shutting down the machines. For the inspector’s convenience, the statistician would like the rejection region to have the form, “Reject H0 if the number of defective parts is C or more.” Find the value of C that will make the significance level (approximately) .05.