Before opening a new location, franchise companies conduct market research to determine if sufficient demand exists for their products. A national sandwich chain recently conducted a survey to investigate opening a franchise in a particular town. Among 300 households contacted through random-digit dialing, 198 respondents indicated they would patronize this shop.

a. Let p = the proportion of all households in this town that would patronize the sandwich franchise. Calculate and interpret a 95% lower confidence bound for p.

b. From years of marketing experience, the company knows they need more than 5000 households in the population to patronize the shop—this accounts for competing local businesses and variation in frequency of visitation by potential patrons. This particular town has 7700 households. Determine a 95% lower confidence bound for the number of households that will eat at the new store. Can the company be confident they will have enough customers?

c. Imagine the company ignored sampling variability and simply used the sample proportion from the survey to determine the expected number of customers (rather than the lower confidence bound). Would that change their opinion regarding the viability of the new location? Explain.