Two machines A and B are set to produce ball bearings to fit an automotive part. Management of RPK Inc. must decide which machine to lease. They requested and got production records of the two machines. The diameter of the bearings is allowed to vary within a range of plus or minus 0.003 inches of the required diameter. Any deviation beyond 0.003 inches of the required diameter is considered substantial. Sample records indicate that when machine A was run 200 times, 2 bearings were found to substantially deviate from the required diameter. When machine B was run 200 times, 9 bearings were found to substantially deviate from the required diameter. Machine A is 4 times as expensive as machine B. Management will only lease machine A if the proportion of time its ball bearings substantially deviate from the required diameter is more than 1.36% smaller than the proportion of time machine B’s ball bearings substantially deviate from the required diameter. 

Required: Conduct a hypothesis test to determine if management should lease machine A. Please show your calculations.