Question

A 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 lost to theft in the stores.

​(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?

The​ 95% confidence interval for the expected number of thefts with the decoy cameras is____ to _____.

The​ 95% confidence interval for the expected number of thefts without the decoy cameras is____to ____.

​(Round to two decimal places as​ needed.)

​(c). The​ 95% t interval for the mean differences in number of thefts is about ____to ____.

Lost to Theft (decoy)   Lost to Theft (control)
49,310   84,411
70,076   66,951
43,239   35,741
34,315   58,600
33,189   31,978
29,852   20,725
87,706   97,843
45,783   20,652
27,380   55,888
33,570   42,624
87,648   84,060
41,451   22,644
55,259   103,200
55,523   77,005
46,891   75,263
67,491   87,289
51,398   89,549
73,057   92,136
34,700   37,265
40,101   60,556

Answer 1