The "arbitrary or capricious" test is a very forgiving standard that asks little more than whether an agency's decision is supported by a “rational connection between the facts found and the choice made.” Bowman Transportation, Inc. v. Arkansas-Best Freight System, Inc., 419 U.S. 281, 285 (1974).
Using the standard, a reviewing court will not ask whether the decision was wise or unwise, whether a policy will be effective or ineffective, or whether another decision would have better achieved the agency's goals; it will merely ask whether the agency has adequately reviewed the available evidence, considered its available options and explained its decision:
A reviewing court may not set aside an agency rule that is rational, based on consideration of the relevant factors, and within the scope of the authority delegated to the agency by the statute. ... The scope of review under the "arbitrary and capricious" standard is narrow and a court is not to substitute its judgment for that of the agency. Nevertheless, the agency must examine the relevant data and articulate a satisfactory explanation for its action including a "rational connection between the facts found and the choice made."
Motor Vehicle Manufacturers Assoc. of the United States, Inc. v. State Farm Mutual Auto. Ins. Co., 463 U.S. 29, 42-43 (1983).
In State Farm, for instance, NHTSA promulgated regulations requiring automobile manufacturers to include passive-restraint systems but then rescinded them based on a conclusion that they it was promoting the use of automatic seat belts at the expense of more effective airbags. State Farm sued, and the courts agreed that the rescission was arbitrary and capricious because NHTSA didn't adequately explain why it believed automatic seatbelts were inadequate and because it failed to consider the possibility of modifying the regulation to simply require the use of airbags.
But this treatment is relatively rare, as the relaxed standard of review naturally results in generally favorable decisions for the agency. For instance, in Bowman, the Interstate Commerce Commission authorized a new group of motor carriers to operate new delivery routes. A trial court blocked the authorization from taking effect because it didn't accept the competitor's evidence that new carriers were unnecessary, but the Supreme Court reversed, holding that the arbitrary-and-capricious standard doesn't allow a reviewing court to second-guess an agency based on its own opinion of what evidence was the most persuasive or what decision would have been the most prudent:
The Commission, of course, is entitled to conclude that preservation of a competitive structure in a given case is overridden by other interests, but where, as here, the Commission concludes that competition aids in the attainment of the objectives of the national transportation policy, we have no basis for disturbing the Commission's accommodation.