Sampling and Confidence Intervals Mini-Case

Scenario Script

Caption: Mieke, the head of Marketing has heard about you. And at Princess Foods, like much of the rest of the world, the reward for good work is more work.

Mieke: Thank you so much for making time for me. Liwei says that you're a miracle worker...

Caption: Princess Foods Corporation is piloting a new service called "Princess Select," a new premium meal kit service. Subscribers are mailed kits that each contain all the ingredients that a customer would need to make a delicious meal in exactly the right proportions. All the customer needs to do is to follow the provided recipe and a fresh, home-cooked meal is ready in no time. Mieke needs to gauge their interest in this new service and decide whether to market it nationally.

Caption: Mieke has stated that at least 75% of the potential customers must express some desire for the service and, for those who exhibit an interest, the average cost they are willing to pay per two-meal package must be at least $49.00. Mieke insists that you be 95% certain of your findings.

Mieke: Because this is a relatively new service on the market, we need some additional insight into how Princess Select would fit into our customers' lives and what they'd be willing to pay for a service like this. We conducted a survey of 50 potential customers. The memo that includes your findings and recommendations?

In the memo, should be included the raw data and a clear interpretation of the data that justifies the findings. Use the raw data below for memo. Since you only have sample data, you decide to determine confidence intervals.

Of the 50 potential consumers surveyed, 33 expressed an interest in purchasing it. The maximum price each would be willing to pay is shown in the table below. Using the data to answer the following questions: 1. How would you reply to the Mieke's request for information? 2. Should the service be marketed? 3. How large should the sample be if you want to maintain a 95% level of confidence and suffer a maximum error of $2.00 in your estimate of the highest price consumers are willing to pay?

Maximum Prices

47 62 46

42 53 30

54 45 35

65 36 32

54 45 31

36 35 28

38 37 56

35 43 65

43 48 54

37 46 65

54 41 47