Sampling and Confidence Intervals Mini-Case Assignment | Complete Solution

Sampling and Confidence Intervals Mini-Case Assignment

Scenario
Larry, the head of Marketing has heard about you. And at TNH Tires, like much of the rest of the world, the reward for good work is more work.
Larry: Thank you so much for making time for me. Manny says that you’re a miracle worker…
TNH Tires is piloting a new service called “Sports Select,” a new premium sports Tire kit service. Subscribers are mailed kits that each contain all the tires and the parts that a customer would need to put all the tires in their special sport cars. All the customer needs to do is to follow the provided instructions and the they will be driving their new wheels in no time. Larry needs to gauge their interest in this new service and decide whether to market it nationally.
Larry, has stated that at least 85% 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-tire kit package must be at least $47.50. Larry insists that you be 95% certain of your findings.
Larry: Because this is a relatively new service on the market, we need some additional insight into how TNH Tires 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. Can you prepare a memo that includes your findings and recommendations?
Mini-Case
In your memo, you should include the raw data and a clear interpretation of the data that justifies your findings. Use the raw data below to write your memo. Since you only have sample data, you decide to determine confidence intervals.
Of the 50 potential consumers surveyed, 34 expressed an interest in purchasing it. The maximum price each would be willing to pay is shown in the table below.
Using the data, answer the following questions:
1. How would you reply to the Larry’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?