A retail chain is considering installing de-vices 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 demo-graphics. 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 lost to theft in the stores.
(a) Why is it important that all of the stores measure theft during the same time period?
(b) Compute separate 95% confidence intervals for the amount lost to theft with and without the decoy cameras. Is there evidence of a statistically significant difference?
(c) Perform the appropriate comparison of the decoy system versus stores without this potential deter-rent. Is there a statistically significant difference in the average amount lost to theft? Be sure to check the conditions for the method used.