“With Sampling, There Is Too a Free Lunch”—This is a headline that appeared in TheWall Street Journal. The article is about food product samples available at grocery stores. Giving out food samples is expensive and labor-intensive. It clogs supermarket aisles. It is risky. What if a customer tries an item and spits it out on the floor or says the product is awful? It creates litter. Some customers drop toothpicks or small paper cups on the floor or spill the product. However, the budget that companies are willing to spend to have their products sampled is growing. The director of communications for Bigg’s “hypermarket” (a combination grocery and general-merchandise store) says that more than 60% of customers sample products and about 37% of those who sample buy the product.
(a) Let’s test the hypothesis that 60% of customers sample a particular product. What is the null hypothesis? Do you believe that the percentage of customers who sample products is less than, more than, or just different from 60%? What will you use for the alternate hypothesis?
(b) Choose a level of significance a.
(c) Go to a grocery store when special products are being sampled (not just the usual in-house store samples often available at the deli or bakery). Count the number of customers going by the display when a sample is available and the number of customers who try the sample. Be sure the number of customers n is large enough to use the normal distribution to approximate the binomial.
(d) Using your sample data, conclude the hypothesis test. What is your conclusion?
(e) Do you think different food products might have a higher or lower percentage of customers trying them? For instance, does a higher percentage of customers try samples of pizza than samples of yogurt? How could you use statistics to justify your answer?
(f) Do you want to include young children in your sample? Do they pick up items to include in the customer’s basket, or do they just munch the samples?