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 potentially can 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."

To avoid the fine and the public embarrassment that follows after 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 320 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 file titled "Price-Check-Fall". The government inspector will not fine companies that have an error rate of less than 2%.

Question 1

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: Is your estimate a single number or a range of numbers?

Question 2

Based on your answer for Question 1, if an inspector showed up today, would the store manager be 95% confident that the store will pass? Why or why not?

Question 3

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