Final answer:
The best group to survey would be every person buying a ticket to the science museum, as it will provide a comprehensive view of the popularity of each exhibit. Surveying the museum staff or a small group of visitors may not accurately reflect the visitors' opinions.
Step-by-step explanation:
In the given case, the best group to survey to find out which exhibit at a science museum is the most popular would be every person buying a ticket to the science museum. This group includes all visitors to the museum and will give a comprehensive view of the popularity of each exhibit.
In addition to this, surveying the museum staff who set up all the current exhibits may not accurately reflect the visitors' opinions, as their preferences may differ. Surveying every fifth person who leaves the museum one afternoon or a group of classmates may not be representative of all museum visitors.