Amazon.com Inc. won a lottery to decide which federal appeals court will decide whether it must bargain with a union thousands of workers at a New York City warehouse elected four years ago.

The company selected the US Court of Appeals for the Fifth Circuit to review the National Labor Relations Board ruling that the company violated its legal obligation to negotiate with the union.

The Fifth Circuit is known for its conservative judges and hostility to administrative agencies. The NLRB won 62% of cases challenging its decisions in the Fifth Circuit over the past five years, one of the …