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?

What table?

I always try to check my receipt.

To determine whether the error rates are the same for regular-priced items and advertised-special items, you can conduct a hypothesis test.

Here's a step-by-step guide on how to perform the hypothesis test:

1. State the null hypothesis (H₀) and alternative hypothesis (H₁):
- Null Hypothesis (H₀): The error rates for regular-priced items and advertised-special items are the same.
- Alternative Hypothesis (H₁): The error rates for regular-priced items and advertised-special items are different.

2. Choose the significance level (alpha) to determine the critical value. Common choices for alpha are 0.01, 0.05, or 0.10. Let's assume alpha = 0.05 for this example.

3. Calculate the test statistic. In this case, you can use a chi-square test statistic to compare the observed frequencies of overcharges and the expected frequencies under the assumption that there is no difference in error rates.

4. Determine the critical value(s) based on the chi-square distribution for your chosen significance level (alpha) and the degrees of freedom. The degrees of freedom will be (number of categories - 1).

5. Compare the test statistic to the critical value(s). If the test statistic is larger than the critical value(s), you reject the null hypothesis.

6. Calculate the p-value associated with the test statistic. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. If the p-value is less than or equal to the chosen significance level (alpha), you reject the null hypothesis.

7. Make a conclusion based on the results. If you reject the null hypothesis, it suggests that the error rates for regular-priced items and advertised-special items are different. If you fail to reject the null hypothesis, it suggests that there is not enough evidence to conclude a difference in error rates.

To address the second part of your question, if consumers believe that disproportionately more overcharges occur with advertised special items, their behavior might change in several ways. They might become more cautious about purchasing advertised-special items, leading to a decrease in sales or demand for these items. Additionally, consumers might actively verify the prices of advertised-special items at the checkout counter or through different means, such as price-checking apps or comparing prices at different stores. This increased vigilance could result in longer checkout times and potentially impact consumer satisfaction and trust in the store's scanning system. Ultimately, consumers' beliefs about error rates could influence their purchasing decisions, perception of the store's credibility, and overall shopping behavior.