Developing a Sampling Plan for a New Menu Initiative Survey Owners of the Santa Fe Grill realize that in order to remain competitive in the restaurant industry, new menu items need to be introduced periodically to provide variety for current customers and to attract new customers. Recognizing this, the owners of the Santa Fe Grill believe three issues need to be addressed using marketing research. The first is should the menu be changed to include items beyond the traditional southwestern cuisine? For example, should they add items that would be considered standard American, Italian, or European cuisine? Second, regardless of the cuisine to be explored, how many new items $($e$.$g$.,$ appetizers, entr$$es$,$ or desserts$)$ should be included on the survey? And third, what type of sampling plan should be developed for selecting respondents, and who should those respondents be$?$ Should they be current customers, new customers, and$/$or old customers? Hands$-$On Exercise Understanding the importance of sampling and the impact it will have on the validity and accuracy of the research results, the owners have asked the local university if a marketing research class could assist them in this project. Specifically, the owners have posed the following questions that need to be addressed: $1.$ How many questions should the survey contain to adequately address all possible new menu items, including the notion of assessing the desirability of new cuisines? In short, how can it be determined that all necessary items will be included on the survey without the risk of ignoring menu items that may be desirable to potential customers? $2.$ How should the potential respondents be selected for the survey? Should customers be interviewed while they are dining? Should customers be asked to participate in the survey upon exiting the restaurant? Or should a mail or telephone approach be used to collect information from customers$/$noncustomers$?$ Based on the above questions, your task is to develop a procedure to address the following issues: $1.$ How many new menu items can be examined on the survey? Remember, all potential menu possibilities should be assessed but you must have a manageable number of questions so the survey can be performed in a timely and reasonable manner. Specifically, from a list of all possible menu items that can be included on the survey, what is the optimal number of menu items that should be used? Is there a sampling procedure one can use to determine the maximum number of menu items to place on the survey? $2.$ Determine the appropriate sample design. Develop a sample design proposal for the Santa Fe Grill that addresses the following: Should a probability or nonprobability sample be used? Given your answer, what type of sampling design should be employed $($simple random, stratified, convenience, etc.$)?$ Given the sample design suggested, how will potential respondents be selected for the study? Finally, determine the necessary sample size and suggest a plan for selecting the sampling units.