Is Scanner Accuracy the Same for Specials?
In a study of store checkout scanning systems, samples of purchases were used to compare the scanned prices to the posted prices. The accompanying table summarizes results for a sample of 819 items. When stores use scanners to check out items, are the error rates the same for regular-priced items as they are for advertised-special items? How might the behavior of consumers change if they believe that disproportionately more overcharges occur with advertised special items?Regular Price Items Advertised special
Undercharged 20 7
Overcharged 15 29
Correct price 384 364
Use the Chi-square (X^2) method.
X^2 = ∑ (O-E)^2/E, where O = observed frequency and E = expected frequency.
∑ = sum of all the cells.
E = (column total * row total)/grand total
df = n - 1, where n = number of cells
Look up value in X^2 table in the back of your textbook.
To determine if the error rates are the same for regular-priced items as they are for advertised-special items, we can compare the proportions of undercharged, overcharged, and correctly priced items for each category.
First, let's calculate the proportions for regular-priced items:
- Undercharged: 20/819 = 0.024 (or 2.4%)
- Overcharged: 15/819 = 0.018 (or 1.8%)
- Correct price: 384/819 = 0.469 (or 46.9%)
Now, let's calculate the proportions for advertised-special items:
- Undercharged: 7/819 = 0.009 (or 0.9%)
- Overcharged: 29/819 = 0.035 (or 3.5%)
- Correct price: 364/819 = 0.445 (or 44.5%)
Comparing the error rates, we can see that the proportions of overcharged items are higher for advertised-special items (3.5% vs. 1.8% for regular-priced items). However, the proportion of undercharged items is lower for advertised-special items (0.9% vs. 2.4% for regular-priced items). The proportion of correctly priced items is similar for both categories (44.5% for advertised-special items vs. 46.9% for regular-priced items).
Based on these results, we can conclude that the error rates are not the same for regular-priced items and advertised-special items. There is a higher proportion of overcharges for advertised-special items in this study.
If consumers believe that disproportionately more overcharges occur with advertised special items, it may impact their behavior. They may be more vigilant in checking the prices of advertised-special items before purchase or may choose to avoid purchasing such items altogether. This perception could have implications for consumer trust and the store's reputation, as customers may become more skeptical or less likely to trust advertised-special prices.