retail chain is considering installing devices that resemble cameras to deter shoplifting. The devices only look like$$ cameras, saving the expense of wiring and recording video. To test the benefit of this decoy$$ system, it picked $40$ stores, with half to get the decoy and the other half to serve as comparison group$($control group$).$ Stores were matched based on typical levels of$$ sales, local market$$ size, and demographics. The comparison lasted for $3$ months during the summer. At the end of the$$ period, the retailer used its inventory system to compute the amounts