A paper company manufactures cardboard boxes. The company wishes to investigate the effects of four production methods on the number of defective boxes produced in an hour. The company randomly selects three machine operators and trains each operator thoroughly to use all four production methods. Then each operator will produce boxes for one hour using each of the four production methods. Test the null hypothesis that the population mean number of defective boxes is the same for the four production methods. Use the output below to answer the following questions. Use a significance level of 0.05 to conduct all hypothesis tests and construct confidence intervals.

Analysis of Variance Sum of Source DF Squares Mean Square F Ratio Prob > F METHOD 3 112.66667 37.5556 79.5294 <.0001 operator error c. total ordered differences report level difference std err dif lower cl upper method2 method4 method1 method3 method o none of the methods differ>