A city wants to estimate the mean time (in minutes) that all city bus riders wait at stops during weekday mornings. The transit office randomly selects 30 bus stops from a complete list of all stops in the city and posts an employee at each selected stop on a Tuesday from 7:00–9:00 a.m. to record wait times for every rider who arrives during that window. Which statement best describes the sample representativeness?
- The sample is likely representative of weekday morning bus riders in the city because the bus stops were selected using a random method from the full list. (correct answer)
- The sample is not representative because only 30 stops were used; a representative sample must include at least 100 stops.
- The sample is not representative because the riders were not randomly assigned to different bus stops.
- The sample is representative of all city residents because bus riders are a random subset of residents.
- The sample is biased because the employees recorded every rider at the selected stops, which overrepresents frequent riders.
Explanation: This question assesses understanding of cluster sampling and its representativeness. The transit office used proper random sampling by randomly selecting 30 bus stops from a complete list, making this a cluster sample where each stop is a cluster. Recording all riders at selected stops during the specified time window captures the full variation at those locations. While the sample only represents Tuesday morning riders (not all times/days), it is representative of weekday morning bus riders because the stops were randomly selected. The key principle is that random selection of sampling units (here, bus stops) from a complete frame helps ensure representativeness. This differs from convenience sampling where locations would be chosen for ease rather than randomly.