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The items for sale in many retail stores ring up differently at the cash register than the price marked on the shelf. This goes unnoticed by many consumers. But, whether the mistakes are intentional or not, the retailers get checked by government inspectors (for overcharges only) and can potentially be fined for the mistakes if their error rate is high enough. The retailers also run the risk of receiving bad publicity through the press. As an example, in one such inspection: “during Walmart’s second inspection, the price of a ceiling fan was off by $30. The shelf price listed the fan at $19.99, but it rang up as $49.97 at the register.” For more, read: Inspector: One in 10 NC stores ring up wrong prices. (https://www.wral.com/inspector-one-in-10-nc-stores-ring-up-wrong-prices/10413522/)

To avoid the fine and the public embarrassment that follows for being caught, each retailer will self-inspect their records. They use the same process as the government inspectors, random items are selected for cross checking. In a recent self-check, the store manager had her employees take 230 different items which were picked at random for cross check. The employees recorded the shelf price and the price that appeared on the cash register – you can find these results in file “Price-Check”. The government inspector will not fine companies that have an error rate of less than 2%.

1. Based on the data in this last study, what is the estimate of proportion of items that will ring up at higher prices?

• If an inspector showed up today, will the store manager be 95% confident that the store will pass? Why, or why not?

• If the manager wants to have a margin error of 0.5% (.005), then how many items need to be crossed checked?

• The manager doesn’t believe she has the resources to do as many cross checks to ensure a margin of error of 0.5%. She wonders if she will be able to defend her store against fines based on the average amount customers are being wrongly charged (either over or under charged).

• What is the maximum overcharge for an item in this study? Was there a customer who was undercharged? If yes, how large was the highest undercharge?
• What is the 95% confidence interval for mean dollar amount of incorrect charges for this data set?
• If the inspector’s sample results in an error rate of 2.7% of items being overcharged, do you think showing the average error (accounting for both undercharges and overcharges) will help her avoid getting fined?
• Should she do a larger study to be sure she can pass inspection? The fine for not passing an inspection is about $1000, followed by a repeated inspection (for example : “Walmart on New Hope Church Road in Raleigh, for example, failed three consecutive inspections, ringing up almost $5,000 in fines before finally passing.” Read Inspector: One in 10 NC stores ring up wrong prices). Explain your answer. 

https://www.wral.com/inspector-one-in-10-nc-stores-ring-up-wrong-prices/10413522/