Which event involves testing a cowboy's ability to stay on a bucking horse?

Saddle bronc riding involves testing a cowboy's ability to stay on a bucking horse. In this event, the rider must maintain their balance and stay on the horse for a required amount of time while the horse performs various bucking movements. It is a traditional rodeo event that showcases both the skill of the rider and the bucking ability of the horse.

In saddle bronc riding, the rider uses a specialized saddle that has no horn, which allows for more freedom of movement compared to other riding styles. The rider is scored based on technique and the horse's performance, highlighting the important aspects of riding dynamics and control.

The other events, such as barrel racing, team roping, and steer wrestling, focus on different skills and techniques. Barrel racing is a timed event concentrating on speed and agility around barrels. Team roping involves two cowboys working together to rope a steer, requiring teamwork and precision. Steer wrestling tests a cowboy's ability to throw a steer to the ground after jumping off a horse.

Each event has its distinct challenges and showcases specific skills related to rodeo, but saddle bronc riding is uniquely centered on the challenge of remaining on a bucking horse, making it the correct answer.