Question: An investigator wants to study the relationship between a child's age, number of siblings, and the dollar amount of the child's Christmas list presented to Santa Claus. She also wants to estimate the total number of children that visit Santa Claus and the total dollar amount of all children's requests. It would be very difficult to construct a sampling frame of children who will visit Santa Claus between December 1 and 24, but the investigator has a list of shopping malls and stores in which Santa will appear in the city, as well as the times that Santa will be at each location. The Santa sites are divided into four categories: 23 department stores, 19 discount stores, 15 toy stores, and 5 shopping malls. The investigator wants you to help design the sample of children.
a What questions would you ask the investigator to clarify the problem?
b Assuming any answers you like to the questions you asked, suggest a design for the survey.
c How will your survey design affect the regression analysis of the data? How do you propose to analyze the data? Are there other explanatory variables that you would suggest to the investigator?