Before the taping of the public affairs program "Why in the World" last week, 14 high school seniors from Prince George's County primped and rehearsed their lines as if they were social studies' answer to the cast of "Fame."

"Why in the World" has students ask experts about topics ranging from housing for the poor to the American love affair with space. It is a production of Satellite Educational Services and public broadcasting station KCET in association with Washington area station WETA, also part of the public broadcasting network.

The taping of two segments of "Why in the World" last week in WETA's Shirlington studio culminated a week of preparation by students and faculty sponsors from Largo Senior and Eleanor Roosevelt high schools.

Parents and fellow students tuned in two days later to watch the young people question congressional budget director Alice Rivlin on the fine points of the budget-making process. They also watched later in the week when WETA aired the second taping, in which the students asked U.S. Ambassador-at-Large Vernon Walters about the art of diplomacy.

Robert Getzenberg, treasurer of his senior class at Eleanor Roosevelt High School, sat stiffly under the hot lights, knitted his eyebrows to achieve a look of stern inquiry, and looked at the woman who has directed the Congressional Budget Office since l975.

"Why," he asked, echoing a conviction that he discussed at length with his father, an accountant for the Securities and Exchange Commission, "can't the Congress bring the budget in line with revenues?"

Priorities, Rivlin responded. She cited the difficulties of cutting programs during an election year, decreased revenues in a slow economy, reluctance to increase taxes. She looked at Getzenberg for a follow-up, but he was busy formulating his next question, and Kathi Prahinski, a majorette from Roosevelt, wanted to know how much could realistically be cut from defense.

Five minutes later, Getzenberg was back. What about the budgeting proposals? Is the government playing too great a role in our economy? Is government regulation the cause of current levels of inflation?

After the taping, Rivlin said she was not the least bit surprised by the questions. After all, they were the kind she gets all the time from professionals.

"Why in the World" was conceived by CBS newsman Walter Cronkite, and has been airing for just over a year. Cronkite called the show "the realization of a dream of mine, to use national television to show the link between the classroom and current events."

In early November, executive producer Barbara Barnes brought the taping from California to WETA's Shirlington studio to tap the area's political luminaries as subjects for the students.

In the eight segments that have been aired since "Why in the World" came to Washington, the show's staff has drawn some of the sharpest students from the District, Northern Virginia, and suburban Maryland. How do they compare with Barnes' West Coast student guests?

"I think they're more politically aware," Barnes said. "And as a result, they appear to be more sophisticated. They're very concerned with what's happening in the world.