Reference no: EM133758047

Assignment: Statistics

The items for sale in many retail stores sometimes ring up at a different price at the cash register compared to 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[1].

To avoid the fine and the public embarrassment that follows for being caught, each retailer will self-inspect their records. They typically use the same process as the government inspectors by selecting a random sample of items for cross-checking the register and the shelf prices.

In a recent self-check, the store manager had her employees compare prices on 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 the MS Excel file titled "Price-Check". The government inspector will not fine companies that have an error rate of less than 2%.

Task

Question I

Based on the data in this study, what is the estimate of proportion of items that will ring up at higher prices and thus be counted as a violation? (Hint: Should your estimate be a single number or a range to provide appropriate background for managerial decision-making?)

Question II

Based on your answer for Question I, if an inspector showed up today, would the store manager be 95% confident that the store will pass? Why, or why not?

Question III

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

Question IV

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 has noticed that in the items checked, some items are ringing up for less at the cash register, so technically, a customer could end up with a bill that is less than what they were expecting. She wonders if she would be able to defend her store against fines based on the average amount customers are being wrongly charged (either over- or undercharged).