Suppose that a restaurant owner wants to investigate whether the type of music played in the background affects how much customers spend on their meals. The owner plans to play classical music on some evenings and contemporary music on other evenings for a total of two weeks, comparing the amounts spent by customers on those evenings. Th e owner is considering three ways to design the study:
• Plan 1: Flip a coin for each evening. If the coin lands heads, play classical music. If the coin lands tails, play contemporary music.
• Plan 2: Write “classical” on seven index cards and “contemporary” on seven index cards. Shuffle the cards well.

Record the order of “classical” and “contemporary” on the cards and play the music in that order over the 14 days.
• Plan 3: Flip a coin for each evening of the first week. If the coin lands heads, play classical music. If the coin lands tails, play contemporary music. Then for each day in the second week, play the other kind of music from what was played on that day in the first week.
a. Identify the explanatory and response variables in this study. Also classify the variables as categorical or quantitative.
b. Is this an observational study or an experiment? Explain how you know.
c. Which of these plans is a matched pairs design?

d. Why might the matched pairs design be better than a completely randomized design in this context?